(2x-3)*(2x-3)+(2x+3)*(2x+3)=8x*(x+2)

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Solution for (2x-3)*(2x-3)+(2x+3)*(2x+3)=8x*(x+2) equation:


Simplifying
(2x + -3)(2x + -3) + (2x + 3)(2x + 3) = 8x(x + 2)

Reorder the terms:
(-3 + 2x)(2x + -3) + (2x + 3)(2x + 3) = 8x(x + 2)

Reorder the terms:
(-3 + 2x)(-3 + 2x) + (2x + 3)(2x + 3) = 8x(x + 2)

Multiply (-3 + 2x) * (-3 + 2x)
(-3(-3 + 2x) + 2x * (-3 + 2x)) + (2x + 3)(2x + 3) = 8x(x + 2)
((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) + (2x + 3)(2x + 3) = 8x(x + 2)
((9 + -6x) + 2x * (-3 + 2x)) + (2x + 3)(2x + 3) = 8x(x + 2)
(9 + -6x + (-3 * 2x + 2x * 2x)) + (2x + 3)(2x + 3) = 8x(x + 2)
(9 + -6x + (-6x + 4x2)) + (2x + 3)(2x + 3) = 8x(x + 2)

Combine like terms: -6x + -6x = -12x
(9 + -12x + 4x2) + (2x + 3)(2x + 3) = 8x(x + 2)

Reorder the terms:
9 + -12x + 4x2 + (3 + 2x)(2x + 3) = 8x(x + 2)

Reorder the terms:
9 + -12x + 4x2 + (3 + 2x)(3 + 2x) = 8x(x + 2)

Multiply (3 + 2x) * (3 + 2x)
9 + -12x + 4x2 + (3(3 + 2x) + 2x * (3 + 2x)) = 8x(x + 2)
9 + -12x + 4x2 + ((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 8x(x + 2)
9 + -12x + 4x2 + ((9 + 6x) + 2x * (3 + 2x)) = 8x(x + 2)
9 + -12x + 4x2 + (9 + 6x + (3 * 2x + 2x * 2x)) = 8x(x + 2)
9 + -12x + 4x2 + (9 + 6x + (6x + 4x2)) = 8x(x + 2)

Combine like terms: 6x + 6x = 12x
9 + -12x + 4x2 + (9 + 12x + 4x2) = 8x(x + 2)

Reorder the terms:
9 + 9 + -12x + 12x + 4x2 + 4x2 = 8x(x + 2)

Combine like terms: 9 + 9 = 18
18 + -12x + 12x + 4x2 + 4x2 = 8x(x + 2)

Combine like terms: -12x + 12x = 0
18 + 0 + 4x2 + 4x2 = 8x(x + 2)
18 + 4x2 + 4x2 = 8x(x + 2)

Combine like terms: 4x2 + 4x2 = 8x2
18 + 8x2 = 8x(x + 2)

Reorder the terms:
18 + 8x2 = 8x(2 + x)
18 + 8x2 = (2 * 8x + x * 8x)
18 + 8x2 = (16x + 8x2)

Add '-8x2' to each side of the equation.
18 + 8x2 + -8x2 = 16x + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
18 + 0 = 16x + 8x2 + -8x2
18 = 16x + 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
18 = 16x + 0
18 = 16x

Solving
18 = 16x

Solving for variable 'x'.

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

Add '-16x' to each side of the equation.
18 + -16x = 16x + -16x

Combine like terms: 16x + -16x = 0
18 + -16x = 0

Add '-18' to each side of the equation.
18 + -18 + -16x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -16x = 0 + -18
-16x = 0 + -18

Combine like terms: 0 + -18 = -18
-16x = -18

Divide each side by '-16'.
x = 1.125

Simplifying
x = 1.125

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