(2x-1)(2x-1)+5=4x(x-2)-2(2x+1)

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Solution for (2x-1)(2x-1)+5=4x(x-2)-2(2x+1) equation:


Simplifying
(2x + -1)(2x + -1) + 5 = 4x(x + -2) + -2(2x + 1)

Reorder the terms:
(-1 + 2x)(2x + -1) + 5 = 4x(x + -2) + -2(2x + 1)

Reorder the terms:
(-1 + 2x)(-1 + 2x) + 5 = 4x(x + -2) + -2(2x + 1)

Multiply (-1 + 2x) * (-1 + 2x)
(-1(-1 + 2x) + 2x * (-1 + 2x)) + 5 = 4x(x + -2) + -2(2x + 1)
((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + 5 = 4x(x + -2) + -2(2x + 1)
((1 + -2x) + 2x * (-1 + 2x)) + 5 = 4x(x + -2) + -2(2x + 1)
(1 + -2x + (-1 * 2x + 2x * 2x)) + 5 = 4x(x + -2) + -2(2x + 1)
(1 + -2x + (-2x + 4x2)) + 5 = 4x(x + -2) + -2(2x + 1)

Combine like terms: -2x + -2x = -4x
(1 + -4x + 4x2) + 5 = 4x(x + -2) + -2(2x + 1)

Reorder the terms:
1 + 5 + -4x + 4x2 = 4x(x + -2) + -2(2x + 1)

Combine like terms: 1 + 5 = 6
6 + -4x + 4x2 = 4x(x + -2) + -2(2x + 1)

Reorder the terms:
6 + -4x + 4x2 = 4x(-2 + x) + -2(2x + 1)
6 + -4x + 4x2 = (-2 * 4x + x * 4x) + -2(2x + 1)
6 + -4x + 4x2 = (-8x + 4x2) + -2(2x + 1)

Reorder the terms:
6 + -4x + 4x2 = -8x + 4x2 + -2(1 + 2x)
6 + -4x + 4x2 = -8x + 4x2 + (1 * -2 + 2x * -2)
6 + -4x + 4x2 = -8x + 4x2 + (-2 + -4x)

Reorder the terms:
6 + -4x + 4x2 = -2 + -8x + -4x + 4x2

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

Add '-4x2' to each side of the equation.
6 + -4x + 4x2 + -4x2 = -2 + -12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -4x + 0 = -2 + -12x + 4x2 + -4x2
6 + -4x = -2 + -12x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -4x = -2 + -12x + 0
6 + -4x = -2 + -12x

Solving
6 + -4x = -2 + -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.
6 + -4x + 12x = -2 + -12x + 12x

Combine like terms: -4x + 12x = 8x
6 + 8x = -2 + -12x + 12x

Combine like terms: -12x + 12x = 0
6 + 8x = -2 + 0
6 + 8x = -2

Add '-6' to each side of the equation.
6 + -6 + 8x = -2 + -6

Combine like terms: 6 + -6 = 0
0 + 8x = -2 + -6
8x = -2 + -6

Combine like terms: -2 + -6 = -8
8x = -8

Divide each side by '8'.
x = -1

Simplifying
x = -1

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