(6x+3y)(4x-5y)=

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Solution for (6x+3y)(4x-5y)= equation: 


Simplifying
(6x + 3y)(4x + -5y) = 0

Multiply (6x + 3y) * (4x + -5y)
(6x * (4x + -5y) + 3y * (4x + -5y)) = 0
((4x * 6x + -5y * 6x) + 3y * (4x + -5y)) = 0

Reorder the terms:
((-30xy + 24x2) + 3y * (4x + -5y)) = 0
((-30xy + 24x2) + 3y * (4x + -5y)) = 0
(-30xy + 24x2 + (4x * 3y + -5y * 3y)) = 0
(-30xy + 24x2 + (12xy + -15y2)) = 0

Reorder the terms:
(-30xy + 12xy + 24x2 + -15y2) = 0

Combine like terms: -30xy + 12xy = -18xy
(-18xy + 24x2 + -15y2) = 0

Solving
-18xy + 24x2 + -15y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6xy + 8x2 + -5y2) = 0

Factor a trinomial.
3((4x + -5y)(2x + y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4x + -5y)' equal to zero and attempt to solve:

Simplifying
4x + -5y = 0

Solving
4x + -5y = 0

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

Add '5y' to each side of the equation.
4x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4x + 0 = 0 + 5y
4x = 0 + 5y
Remove the zero:
4x = 5y

Divide each side by '4'.
x = 1.25y

Simplifying
x = 1.25y

Subproblem 2
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
Solution
x = {1.25y, -0.5y}

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