(4x-6y)(2x+6y)=

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Solution for (4x-6y)(2x+6y)= equation:


Simplifying
(4x + -6y)(2x + 6y) = 0

Multiply (4x + -6y) * (2x + 6y)
(4x * (2x + 6y) + -6y * (2x + 6y)) = 0
((2x * 4x + 6y * 4x) + -6y * (2x + 6y)) = 0

Reorder the terms:
((24xy + 8x2) + -6y * (2x + 6y)) = 0
((24xy + 8x2) + -6y * (2x + 6y)) = 0
(24xy + 8x2 + (2x * -6y + 6y * -6y)) = 0
(24xy + 8x2 + (-12xy + -36y2)) = 0

Reorder the terms:
(24xy + -12xy + 8x2 + -36y2) = 0

Combine like terms: 24xy + -12xy = 12xy
(12xy + 8x2 + -36y2) = 0

Solving
12xy + 8x2 + -36y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3xy + 2x2 + -9y2) = 0

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

Ignore the factor 4.

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 '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3y

Solution

x = {1.5y, -3y}

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