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

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


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

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

Reorder the terms:
((24xy + 16x2) + -6y * (4x + 6y)) + (4x + 6y)(4x + -6y) = 0
((24xy + 16x2) + -6y * (4x + 6y)) + (4x + 6y)(4x + -6y) = 0
(24xy + 16x2 + (4x * -6y + 6y * -6y)) + (4x + 6y)(4x + -6y) = 0
(24xy + 16x2 + (-24xy + -36y2)) + (4x + 6y)(4x + -6y) = 0

Reorder the terms:
(24xy + -24xy + 16x2 + -36y2) + (4x + 6y)(4x + -6y) = 0

Combine like terms: 24xy + -24xy = 0
(0 + 16x2 + -36y2) + (4x + 6y)(4x + -6y) = 0
(16x2 + -36y2) + (4x + 6y)(4x + -6y) = 0

Multiply (4x + 6y) * (4x + -6y)
16x2 + -36y2 + (4x * (4x + -6y) + 6y * (4x + -6y)) = 0
16x2 + -36y2 + ((4x * 4x + -6y * 4x) + 6y * (4x + -6y)) = 0

Reorder the terms:
16x2 + -36y2 + ((-24xy + 16x2) + 6y * (4x + -6y)) = 0
16x2 + -36y2 + ((-24xy + 16x2) + 6y * (4x + -6y)) = 0
16x2 + -36y2 + (-24xy + 16x2 + (4x * 6y + -6y * 6y)) = 0
16x2 + -36y2 + (-24xy + 16x2 + (24xy + -36y2)) = 0

Reorder the terms:
16x2 + -36y2 + (-24xy + 24xy + 16x2 + -36y2) = 0

Combine like terms: -24xy + 24xy = 0
16x2 + -36y2 + (0 + 16x2 + -36y2) = 0
16x2 + -36y2 + (16x2 + -36y2) = 0

Reorder the terms:
16x2 + 16x2 + -36y2 + -36y2 = 0

Combine like terms: 16x2 + 16x2 = 32x2
32x2 + -36y2 + -36y2 = 0

Combine like terms: -36y2 + -36y2 = -72y2
32x2 + -72y2 = 0

Solving
32x2 + -72y2 = 0

Solving for variable 'x'.

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

Add '72y2' to each side of the equation.
32x2 + -72y2 + 72y2 = 0 + 72y2

Combine like terms: -72y2 + 72y2 = 0
32x2 + 0 = 0 + 72y2
32x2 = 0 + 72y2
Remove the zero:
32x2 = 72y2

Divide each side by '32'.
x2 = 2.25y2

Simplifying
x2 = 2.25y2

Take the square root of each side:
x = {-1.5y, 1.5y}

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