(x*2-3y*2)(x*2+7y*2)=

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Solution for (x*2-3y*2)(x*2+7y*2)= equation: 


Simplifying
(x * 2 + -3y * 2)(x * 2 + 7y * 2) = 0

Reorder the terms for easier multiplication:
(2x + -3y * 2)(x * 2 + 7y * 2) = 0

Reorder the terms for easier multiplication:
(2x + -3 * 2y)(x * 2 + 7y * 2) = 0

Multiply -3 * 2
(2x + -6y)(x * 2 + 7y * 2) = 0

Reorder the terms for easier multiplication:
(2x + -6y)(2x + 7y * 2) = 0

Reorder the terms for easier multiplication:
(2x + -6y)(2x + 7 * 2y) = 0

Multiply 7 * 2
(2x + -6y)(2x + 14y) = 0

Multiply (2x + -6y) * (2x + 14y)
(2x * (2x + 14y) + -6y * (2x + 14y)) = 0
((2x * 2x + 14y * 2x) + -6y * (2x + 14y)) = 0

Reorder the terms:
((28xy + 4x2) + -6y * (2x + 14y)) = 0
((28xy + 4x2) + -6y * (2x + 14y)) = 0
(28xy + 4x2 + (2x * -6y + 14y * -6y)) = 0
(28xy + 4x2 + (-12xy + -84y2)) = 0

Reorder the terms:
(28xy + -12xy + 4x2 + -84y2) = 0

Combine like terms: 28xy + -12xy = 16xy
(16xy + 4x2 + -84y2) = 0

Solving
16xy + 4x2 + -84y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4xy + x2 + -21y2) = 0

Factor a trinomial.
4((x + -3y)(x + 7y)) = 0

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(x + 7y)' equal to zero and attempt to solve:

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

Add '-7y' to each side of the equation.
x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
x + 0 = 0 + -7y
x = 0 + -7y
Remove the zero:
x = -7y

Simplifying
x = -7y
Solution
x = {3y, -7y}

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