(x+1)(2x+1)=(x+3)(2x-3)=14
Answers
Answer:
x=1
Step-by-step explanation:
Simplifying
(x + 1)(2x + 1) = (x + 3)(2x + 3) + -14
Reorder the terms:
(1 + x)(2x + 1) = (x + 3)(2x + 3) + -14
Reorder the terms:
(1 + x)(1 + 2x) = (x + 3)(2x + 3) + -14
Multiply (1 + x) * (1 + 2x)
(1(1 + 2x) + x(1 + 2x)) = (x + 3)(2x + 3) + -14
((1 * 1 + 2x * 1) + x(1 + 2x)) = (x + 3)(2x + 3) + -14
((1 + 2x) + x(1 + 2x)) = (x + 3)(2x + 3) + -14
(1 + 2x + (1 * x + 2x * x)) = (x + 3)(2x + 3) + -14
(1 + 2x + (1x + 2x2)) = (x + 3)(2x + 3) + -14
Combine like terms: 2x + 1x = 3x
(1 + 3x + 2x2) = (x + 3)(2x + 3) + -14
Reorder the terms:
1 + 3x + 2x2 = (3 + x)(2x + 3) + -14
Reorder the terms:
1 + 3x + 2x2 = (3 + x)(3 + 2x) + -14
Multiply (3 + x) * (3 + 2x)
1 + 3x + 2x2 = (3(3 + 2x) + x(3 + 2x)) + -14
1 + 3x + 2x2 = ((3 * 3 + 2x * 3) + x(3 + 2x)) + -14
1 + 3x + 2x2 = ((9 + 6x) + x(3 + 2x)) + -14
1 + 3x + 2x2 = (9 + 6x + (3 * x + 2x * x)) + -14
1 + 3x + 2x2 = (9 + 6x + (3x + 2x2)) + -14
Combine like terms: 6x + 3x = 9x
1 + 3x + 2x2 = (9 + 9x + 2x2) + -14
Reorder the terms:
1 + 3x + 2x2 = 9 + -14 + 9x + 2x2
Combine like terms: 9 + -14 = -5
1 + 3x + 2x2 = -5 + 9x + 2x2
Add '-2x2' to each side of the equation.
1 + 3x + 2x2 + -2x2 = -5 + 9x + 2x2 + -2x2
Combine like terms: 2x2 + -2x2 = 0
1 + 3x + 0 = -5 + 9x + 2x2 + -2x2
1 + 3x = -5 + 9x + 2x2 + -2x2
Combine like terms: 2x2 + -2x2 = 0
1 + 3x = -5 + 9x + 0
1 + 3x = -5 + 9x
Solving
1 + 3x = -5 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
1 + 3x + -9x = -5 + 9x + -9x
Combine like terms: 3x + -9x = -6x
1 + -6x = -5 + 9x + -9x
Combine like terms: 9x + -9x = 0
1 + -6x = -5 + 0
1 + -6x = -5
Add '-1' to each side of the equation.
1 + -1 + -6x = -5 + -1
Combine like terms: 1 + -1 = 0
0 + -6x = -5 + -1
-6x = -5 + -1
Combine like terms: -5 + -1 = -6
-6x = -6
Divide each side by '-6'.
x = 1
Simplifying
x = 1