add 2X+3y and 4X-2y
Answers
Simplifying
(2x + 3y)(4x + 2y) = 0
Multiply (2x + 3y) * (4x + 2y)
(2x * (4x + 2y) + 3y * (4x + 2y)) = 0
((4x * 2x + 2y * 2x) + 3y * (4x + 2y)) = 0
Reorder the terms:
((4xy + 8x2) + 3y * (4x + 2y)) = 0
((4xy + 8x2) + 3y * (4x + 2y)) = 0
(4xy + 8x2 + (4x * 3y + 2y * 3y)) = 0
(4xy + 8x2 + (12xy + 6y2)) = 0
Reorder the terms:
(4xy + 12xy + 8x2 + 6y2) = 0
Combine like terms: 4xy + 12xy = 16xy
(16xy + 8x2 + 6y2) = 0
Solving
16xy + 8x2 + 6y2 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '2'.
2(8xy + 4x2 + 3y2) = 0
Factor a trinomial.
2((2x + y)(2x + 3y)) = 0
Ignore the factor 2.
Subproblem 1
Set the factor '(2x + y)' equal to zero and attempt to solve:
Simplifying
2x + y = 0
Solving
2x + y = 0
Move all terms containing x to the left, all other terms to the right.
Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y
Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y
Divide each side by '2'.
x = -0.5y
Simplifying
x = -0.5y
Subproblem 2
Set the factor '(2x + 3y)' equal to zero and attempt to solve:
Simplifying
2x + 3y = 0
Solving
2x + 3y = 0
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y
Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y
Divide each side by '2'.
x = -1.5y
Simplifying
x = -1.5y
Solution
x = {-0.5y, -1.5y}
Step-by-step explanation:
(2x+3y)+(4x-2y)
=2x+3y+4x-2y
= 6x-y