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

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


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

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

Reorder the terms:
((25xy + 25x2) + -6y * (5x + 5y)) = 0
((25xy + 25x2) + -6y * (5x + 5y)) = 0
(25xy + 25x2 + (5x * -6y + 5y * -6y)) = 0
(25xy + 25x2 + (-30xy + -30y2)) = 0

Reorder the terms:
(25xy + -30xy + 25x2 + -30y2) = 0

Combine like terms: 25xy + -30xy = -5xy
(-5xy + 25x2 + -30y2) = 0

Solving
-5xy + 25x2 + -30y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1xy + 5x2 + -6y2) = 0

Factor a trinomial.
5((5x + -6y)(x + y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(5x + -6y)' equal to zero and attempt to solve:

Simplifying
5x + -6y = 0

Solving
5x + -6y = 0

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

Add '6y' to each side of the equation.
5x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
5x + 0 = 0 + 6y
5x = 0 + 6y
Remove the zero:
5x = 6y

Divide each side by '5'.
x = 1.2y

Simplifying
x = 1.2y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y
Solution
x = {1.2y, -1y}

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