(2x+1)(2x+1)-(2x-1)(2x-1)=(x+6)(x+6)-(x)(x)

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Solution for (2x+1)(2x+1)-(2x-1)(2x-1)=(x+6)(x+6)-(x)(x) equation: 


Simplifying
(2x + 1)(2x + 1) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
(1 + 2x)(2x + 1) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
(1 + 2x)(1 + 2x) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Multiply (1 + 2x) * (1 + 2x)
(1(1 + 2x) + 2x * (1 + 2x)) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)
((1 * 1 + 2x * 1) + 2x * (1 + 2x)) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)
((1 + 2x) + 2x * (1 + 2x)) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)
(1 + 2x + (1 * 2x + 2x * 2x)) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)
(1 + 2x + (2x + 4x2)) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Combine like terms: 2x + 2x = 4x
(1 + 4x + 4x2) + -1(2x + -1)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
1 + 4x + 4x2 + -1(-1 + 2x)(2x + -1) = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
1 + 4x + 4x2 + -1(-1 + 2x)(-1 + 2x) = (x + 6)(x + 6) + -1(x)(x)

Multiply (-1 + 2x) * (-1 + 2x)
1 + 4x + 4x2 + -1(-1(-1 + 2x) + 2x * (-1 + 2x)) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + -1((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + -1((1 + -2x) + 2x * (-1 + 2x)) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + -1(1 + -2x + (-1 * 2x + 2x * 2x)) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + -1(1 + -2x + (-2x + 4x2)) = (x + 6)(x + 6) + -1(x)(x)

Combine like terms: -2x + -2x = -4x
1 + 4x + 4x2 + -1(1 + -4x + 4x2) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + (1 * -1 + -4x * -1 + 4x2 * -1) = (x + 6)(x + 6) + -1(x)(x)
1 + 4x + 4x2 + (-1 + 4x + -4x2) = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
1 + -1 + 4x + 4x + 4x2 + -4x2 = (x + 6)(x + 6) + -1(x)(x)

Combine like terms: 1 + -1 = 0
0 + 4x + 4x + 4x2 + -4x2 = (x + 6)(x + 6) + -1(x)(x)
4x + 4x + 4x2 + -4x2 = (x + 6)(x + 6) + -1(x)(x)

Combine like terms: 4x + 4x = 8x
8x + 4x2 + -4x2 = (x + 6)(x + 6) + -1(x)(x)

Combine like terms: 4x2 + -4x2 = 0
8x + 0 = (x + 6)(x + 6) + -1(x)(x)
8x = (x + 6)(x + 6) + -1(x)(x)

Reorder the terms:
8x = (6 + x)(x + 6) + -1(x)(x)

Reorder the terms:
8x = (6 + x)(6 + x) + -1(x)(x)

Multiply (6 + x) * (6 + x)
8x = (6(6 + x) + x(6 + x)) + -1(x)(x)
8x = ((6 * 6 + x * 6) + x(6 + x)) + -1(x)(x)
8x = ((36 + 6x) + x(6 + x)) + -1(x)(x)
8x = (36 + 6x + (6 * x + x * x)) + -1(x)(x)
8x = (36 + 6x + (6x + x2)) + -1(x)(x)

Combine like terms: 6x + 6x = 12x
8x = (36 + 12x + x2) + -1(x)(x)

Multiply x * x
8x = 36 + 12x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8x = 36 + 12x + 0
8x = 36 + 12x

Solving
8x = 36 + 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
8x + -12x = 36 + 12x + -12x

Combine like terms: 8x + -12x = -4x
-4x = 36 + 12x + -12x

Combine like terms: 12x + -12x = 0
-4x = 36 + 0
-4x = 36

Divide each side by '-4'.
x = -9

Simplifying
x = -9

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