(5x+8y)(4x-6y)=

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Solution for (5x+8y)(4x-6y)= equation: 


Simplifying
(5x + 8y)(4x + -6y) = 0

Multiply (5x + 8y) * (4x + -6y)
(5x * (4x + -6y) + 8y * (4x + -6y)) = 0
((4x * 5x + -6y * 5x) + 8y * (4x + -6y)) = 0

Reorder the terms:
((-30xy + 20x2) + 8y * (4x + -6y)) = 0
((-30xy + 20x2) + 8y * (4x + -6y)) = 0
(-30xy + 20x2 + (4x * 8y + -6y * 8y)) = 0
(-30xy + 20x2 + (32xy + -48y2)) = 0

Reorder the terms:
(-30xy + 32xy + 20x2 + -48y2) = 0

Combine like terms: -30xy + 32xy = 2xy
(2xy + 20x2 + -48y2) = 0

Solving
2xy + 20x2 + -48y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(xy + 10x2 + -24y2) = 0

Factor a trinomial.
2((2x + -3y)(5x + 8y)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5x + 8y)' equal to zero and attempt to solve:

Simplifying
5x + 8y = 0

Solving
5x + 8y = 0

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

Add '-8y' to each side of the equation.
5x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
5x + 0 = 0 + -8y
5x = 0 + -8y
Remove the zero:
5x = -8y

Divide each side by '5'.
x = -1.6y

Simplifying
x = -1.6y
Solution
x = {1.5y, -1.6y}

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