(2x-1)(2x+1)-(3+2x)(4+2x)=1

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Solution for (2x-1)(2x+1)-(3+2x)(4+2x)=1 equation: 


Simplifying
(2x + -1)(2x + 1) + -1(3 + 2x)(4 + 2x) = 1

Reorder the terms:
(-1 + 2x)(2x + 1) + -1(3 + 2x)(4 + 2x) = 1

Reorder the terms:
(-1 + 2x)(1 + 2x) + -1(3 + 2x)(4 + 2x) = 1

Multiply (-1 + 2x) * (1 + 2x)
(-1(1 + 2x) + 2x * (1 + 2x)) + -1(3 + 2x)(4 + 2x) = 1
((1 * -1 + 2x * -1) + 2x * (1 + 2x)) + -1(3 + 2x)(4 + 2x) = 1
((-1 + -2x) + 2x * (1 + 2x)) + -1(3 + 2x)(4 + 2x) = 1
(-1 + -2x + (1 * 2x + 2x * 2x)) + -1(3 + 2x)(4 + 2x) = 1
(-1 + -2x + (2x + 4x2)) + -1(3 + 2x)(4 + 2x) = 1

Combine like terms: -2x + 2x = 0
(-1 + 0 + 4x2) + -1(3 + 2x)(4 + 2x) = 1
(-1 + 4x2) + -1(3 + 2x)(4 + 2x) = 1

Multiply (3 + 2x) * (4 + 2x)
-1 + 4x2 + -1(3(4 + 2x) + 2x * (4 + 2x)) = 1
-1 + 4x2 + -1((4 * 3 + 2x * 3) + 2x * (4 + 2x)) = 1
-1 + 4x2 + -1((12 + 6x) + 2x * (4 + 2x)) = 1
-1 + 4x2 + -1(12 + 6x + (4 * 2x + 2x * 2x)) = 1
-1 + 4x2 + -1(12 + 6x + (8x + 4x2)) = 1

Combine like terms: 6x + 8x = 14x
-1 + 4x2 + -1(12 + 14x + 4x2) = 1
-1 + 4x2 + (12 * -1 + 14x * -1 + 4x2 * -1) = 1
-1 + 4x2 + (-12 + -14x + -4x2) = 1

Reorder the terms:
-1 + -12 + -14x + 4x2 + -4x2 = 1

Combine like terms: -1 + -12 = -13
-13 + -14x + 4x2 + -4x2 = 1

Combine like terms: 4x2 + -4x2 = 0
-13 + -14x + 0 = 1
-13 + -14x = 1

Solving
-13 + -14x = 1

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + -14x = 1 + 13

Combine like terms: -13 + 13 = 0
0 + -14x = 1 + 13
-14x = 1 + 13

Combine like terms: 1 + 13 = 14
-14x = 14

Divide each side by '-14'.
x = -1

Simplifying
x = -1

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