(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 + -1(X2)

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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