(2x+3y)(2x+3y)=5x^2+9y^2+12xy

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Solution for (2x+3y)(2x+3y)=5x^2+9y^2+12xy equation: 


Simplifying
(2x + 3y)(2x + 3y) = 5x2 + 9y2 + 12xy

Multiply (2x + 3y) * (2x + 3y)
(2x * (2x + 3y) + 3y * (2x + 3y)) = 5x2 + 9y2 + 12xy
((2x * 2x + 3y * 2x) + 3y * (2x + 3y)) = 5x2 + 9y2 + 12xy

Reorder the terms:
((6xy + 4x2) + 3y * (2x + 3y)) = 5x2 + 9y2 + 12xy
((6xy + 4x2) + 3y * (2x + 3y)) = 5x2 + 9y2 + 12xy
(6xy + 4x2 + (2x * 3y + 3y * 3y)) = 5x2 + 9y2 + 12xy
(6xy + 4x2 + (6xy + 9y2)) = 5x2 + 9y2 + 12xy

Reorder the terms:
(6xy + 6xy + 4x2 + 9y2) = 5x2 + 9y2 + 12xy

Combine like terms: 6xy + 6xy = 12xy
(12xy + 4x2 + 9y2) = 5x2 + 9y2 + 12xy

Reorder the terms:
12xy + 4x2 + 9y2 = 12xy + 5x2 + 9y2

Add '-12xy' to each side of the equation.
12xy + 4x2 + -12xy + 9y2 = 12xy + 5x2 + -12xy + 9y2

Reorder the terms:
12xy + -12xy + 4x2 + 9y2 = 12xy + 5x2 + -12xy + 9y2

Combine like terms: 12xy + -12xy = 0
0 + 4x2 + 9y2 = 12xy + 5x2 + -12xy + 9y2
4x2 + 9y2 = 12xy + 5x2 + -12xy + 9y2

Reorder the terms:
4x2 + 9y2 = 12xy + -12xy + 5x2 + 9y2

Combine like terms: 12xy + -12xy = 0
4x2 + 9y2 = 0 + 5x2 + 9y2
4x2 + 9y2 = 5x2 + 9y2

Add '-9y2' to each side of the equation.
4x2 + 9y2 + -9y2 = 5x2 + 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
4x2 + 0 = 5x2 + 9y2 + -9y2
4x2 = 5x2 + 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
4x2 = 5x2 + 0
4x2 = 5x2

Solving
4x2 = 5x2

Solving for variable 'x'.

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

Add '-5x2' to each side of the equation.
4x2 + -5x2 = 5x2 + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1x2 = 0

Divide each side by '-1'.
x2 = 0

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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