Question

Solve the equation (x + 2) (x + 3)(x + 8) (x + 12) = 4x^2​

Answer 1

$= > (x + 2)(x + 3)(x + 8)(x + 12) = 4x {}^{2} \\ = > (x {}^{2} + 5x + 6)(x {}^{2} + 20x + 96) = 4x {}^{2} \\ = > x { }^{4} + 20x {}^{3} + 96x {}^{2} + 5x {}^{3} + 100x {}^{2} + 480x + 6x {}^{2} + 120x + 576 = 4x {}^{2} \\ = > x {}^{4} + 25x {}^{3} + 202x {}^{2} + 600x + 576 = 4x {}^{2} \\ = > x {}^{4} + 25x {}^{3} + 198x {}^{2} + 600x + 576 = 0$

Answer 2

Simplifying

(x + 2)(x + 3)(x + 8)(x + 12) = 4x²

Reorder the terms:

(2 + x)(x + 3)(x + 8)(x + 12) = 4x²

Multiply (2 + x) * (3 + x)

(2(3 + x) + x(3 + x))(8 + x)(12 + x) = 4x²

((3 * 2 + x * 2) + x(3 + x))(8 + x)(12 + x) = 4x²

((6 + 2x) + x(3 + x))(8 + x)(12 + x) = 4x²

(6 + 2x + (3 * x + x * x))(8 + x)(12 + x) = 4x²

(6 + 2x + (3x + x2))(8 + x)(12 + x) = 4x²

Combine like terms: 2x + 3x = 5x

(6 + 5x + x2)(8 + x)(12 + x) = 4x²

Multiply (6 + 5x + x2) * (8 + x)

(6(8 + x) + 5x * (8 + x) + x2(8 + x))(12 + x) = 4x²

((8 * 6 + x * 6) + 5x * (8 + x) + x2(8 + x))(12 + x) = 4x²

((48 + 6x) + 5x * (8 + x) + x2(8 + x))(12 + x) = 4x²

(48 + 6x + (8 * 5x + x * 5x) + x2(8 + x))(12 + x) = 4x²

(48 + 6x + (40x + 5x2) + x2(8 + x))(12 + x) = 4x²

(48 + 6x + 40x + 5x2 + (8 * x2 + x * x2))(12 + x) = 4x²

(48 + 6x + 40x + 5x2 + (8x2 + x3))(12 + x) = 4x²

Combine like terms: 6x + 40x = 46x

(48 + 46x + 5x²+ 8x2 + x3)(12 + x) = 4x2

Combine like terms: 5x² + 8x² = 13x²

(48 + 46x + 13x² + x3)(12 + x) = 4x²

Multiply (48 + 46x + 13x²+ x³) * (12 + x)

(48(12 + x) + 46x * (12 + x) + 13x² * (12 + x) + x3(12 + x)) = 4x²

((12 * 48 + x * 48) + 46x * (12 + x) + 13x² * (12 + x) + x³(12 + x)) = 4x²

((576 + 48x) + 46x * (12 + x) + 13x² * (12 + x) + x³(12 + x)) = 4x²

(576 + 48x + (12 * 46x + x * 46x) + 13x²* (12 + x) + x³(12 + x)) = 4x²

(576 + 48x + (552x + 46x2) + 13x² * (12 + x) + x³(12 + x)) = 4x²

(576 + 48x + 552x + 46x² + (12 * 13x² + x * 13x2) + x³(12 + x)) = 4x²

(576 + 48x + 552x + 46x2 + (156x2 + 13x³) + x3(12 + x)) = 4x²

(576 + 48x + 552x + 46x2 + 156x² + 13x³ + (12 * x³ + x * x3)) = 4x²

(576 + 48x + 552x + 46x²+ 156x² + 13x³ + (12x3 + x4)) = 4x²

Combine like terms: 48x + 552x = 600x

(576 + 600x + 46x² + 156x² + 13x³ + 12x³+ x4) = 4x²

Combine like terms: 46x²+ 156x² = 202x²

(576 + 600x + 202x² + 13x³ + 12x³ + x4) = 4x²

Combine like terms: 13x³ + 12x³ = 25x³

(576 + 600x + 202x² + 25x³+ x4) = 4x²

Solving

576 + 600x + 202x² + 25x³ + x4 = 4x²

Solving for variable 'x'.

Reorder the terms:

576 + 600x + 202x² + -4x² + 25x³ + x4 = 4x² + -4x²

Combine like terms: 202x² + -4x² = 198x²

576 + 600x + 198x² + 25x³ + x4 = 4x² + -4x²

Combine like terms: 4x² + -4x² = 0

576 + 600x + 198x² + 25x³ + x4 = 0

The solution to this equation could not be determined.