(4x+3y)(2x-8y)=

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Solution for (4x+3y)(2x-8y)= equation: 


Simplifying
(4x + 3y)(2x + -8y) = 0

Multiply (4x + 3y) * (2x + -8y)
(4x * (2x + -8y) + 3y * (2x + -8y)) = 0
((2x * 4x + -8y * 4x) + 3y * (2x + -8y)) = 0

Reorder the terms:
((-32xy + 8x2) + 3y * (2x + -8y)) = 0
((-32xy + 8x2) + 3y * (2x + -8y)) = 0
(-32xy + 8x2 + (2x * 3y + -8y * 3y)) = 0
(-32xy + 8x2 + (6xy + -24y2)) = 0

Reorder the terms:
(-32xy + 6xy + 8x2 + -24y2) = 0

Combine like terms: -32xy + 6xy = -26xy
(-26xy + 8x2 + -24y2) = 0

Solving
-26xy + 8x2 + -24y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13xy + 4x2 + -12y2) = 0

Factor a trinomial.
2((x + -4y)(4x + 3y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

Move all terms containing x to the left, all other terms to the right.

Add '4y' to each side of the equation.
x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
x + 0 = 0 + 4y
x = 0 + 4y
Remove the zero:
x = 4y

Simplifying
x = 4y

Subproblem 2
Set the factor '(4x + 3y)' equal to zero and attempt to solve:

Simplifying
4x + 3y = 0

Solving
4x + 3y = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.
4x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
4x + 0 = 0 + -3y
4x = 0 + -3y
Remove the zero:
4x = -3y

Divide each side by '4'.
x = -0.75y

Simplifying
x = -0.75y
Solution
x = {4y, -0.75y}

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