2(x-2)(x+2)=(x-4)(x+4)+(x-3)(x+3)+x

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Solution for 2(x-2)(x+2)=(x-4)(x+4)+(x-3)(x+3)+x equation: 


Simplifying
2(x + -2)(x + 2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x

Reorder the terms:
2(-2 + x)(x + 2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x

Reorder the terms:
2(-2 + x)(2 + x) = (x + -4)(x + 4) + (x + -3)(x + 3) + x

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

Combine like terms: -2x + 2x = 0
2(-4 + 0 + x2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x
2(-4 + x2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x
(-4 * 2 + x2 * 2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x
(-8 + 2x2) = (x + -4)(x + 4) + (x + -3)(x + 3) + x

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

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

Multiply (-4 + x) * (4 + x)
-8 + 2x2 = (-4(4 + x) + x(4 + x)) + (x + -3)(x + 3) + x
-8 + 2x2 = ((4 * -4 + x * -4) + x(4 + x)) + (x + -3)(x + 3) + x
-8 + 2x2 = ((-16 + -4x) + x(4 + x)) + (x + -3)(x + 3) + x
-8 + 2x2 = (-16 + -4x + (4 * x + x * x)) + (x + -3)(x + 3) + x
-8 + 2x2 = (-16 + -4x + (4x + x2)) + (x + -3)(x + 3) + x

Combine like terms: -4x + 4x = 0
-8 + 2x2 = (-16 + 0 + x2) + (x + -3)(x + 3) + x
-8 + 2x2 = (-16 + x2) + (x + -3)(x + 3) + x

Reorder the terms:
-8 + 2x2 = -16 + x2 + (-3 + x)(x + 3) + x

Reorder the terms:
-8 + 2x2 = -16 + x2 + (-3 + x)(3 + x) + x

Multiply (-3 + x) * (3 + x)
-8 + 2x2 = -16 + x2 + (-3(3 + x) + x(3 + x)) + x
-8 + 2x2 = -16 + x2 + ((3 * -3 + x * -3) + x(3 + x)) + x
-8 + 2x2 = -16 + x2 + ((-9 + -3x) + x(3 + x)) + x
-8 + 2x2 = -16 + x2 + (-9 + -3x + (3 * x + x * x)) + x
-8 + 2x2 = -16 + x2 + (-9 + -3x + (3x + x2)) + x

Combine like terms: -3x + 3x = 0
-8 + 2x2 = -16 + x2 + (-9 + 0 + x2) + x
-8 + 2x2 = -16 + x2 + (-9 + x2) + x

Reorder the terms:
-8 + 2x2 = -16 + -9 + x + x2 + x2

Combine like terms: -16 + -9 = -25
-8 + 2x2 = -25 + x + x2 + x2

Combine like terms: x2 + x2 = 2x2
-8 + 2x2 = -25 + x + 2x2

Add '-2x2' to each side of the equation.
-8 + 2x2 + -2x2 = -25 + x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + 0 = -25 + x + 2x2 + -2x2
-8 = -25 + x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 = -25 + x + 0
-8 = -25 + x

Solving
-8 = -25 + x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-8 + -1x = -25 + x + -1x

Combine like terms: x + -1x = 0
-8 + -1x = -25 + 0
-8 + -1x = -25

Add '8' to each side of the equation.
-8 + 8 + -1x = -25 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = -25 + 8
-1x = -25 + 8

Combine like terms: -25 + 8 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17

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