(2x-1)(2x+1)+6=4(x-4)(x-4)+3x

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Solution for (2x-1)(2x+1)+6=4(x-4)(x-4)+3x equation:


Simplifying
(2x + -1)(2x + 1) + 6 = 4(x + -4)(x + -4) + 3x

Reorder the terms:
(-1 + 2x)(2x + 1) + 6 = 4(x + -4)(x + -4) + 3x

Reorder the terms:
(-1 + 2x)(1 + 2x) + 6 = 4(x + -4)(x + -4) + 3x

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

Combine like terms: -2x + 2x = 0
(-1 + 0 + 4x2) + 6 = 4(x + -4)(x + -4) + 3x
(-1 + 4x2) + 6 = 4(x + -4)(x + -4) + 3x

Reorder the terms:
-1 + 6 + 4x2 = 4(x + -4)(x + -4) + 3x

Combine like terms: -1 + 6 = 5
5 + 4x2 = 4(x + -4)(x + -4) + 3x

Reorder the terms:
5 + 4x2 = 4(-4 + x)(x + -4) + 3x

Reorder the terms:
5 + 4x2 = 4(-4 + x)(-4 + x) + 3x

Multiply (-4 + x) * (-4 + x)
5 + 4x2 = 4(-4(-4 + x) + x(-4 + x)) + 3x
5 + 4x2 = 4((-4 * -4 + x * -4) + x(-4 + x)) + 3x
5 + 4x2 = 4((16 + -4x) + x(-4 + x)) + 3x
5 + 4x2 = 4(16 + -4x + (-4 * x + x * x)) + 3x
5 + 4x2 = 4(16 + -4x + (-4x + x2)) + 3x

Combine like terms: -4x + -4x = -8x
5 + 4x2 = 4(16 + -8x + x2) + 3x
5 + 4x2 = (16 * 4 + -8x * 4 + x2 * 4) + 3x
5 + 4x2 = (64 + -32x + 4x2) + 3x

Reorder the terms:
5 + 4x2 = 64 + -32x + 3x + 4x2

Combine like terms: -32x + 3x = -29x
5 + 4x2 = 64 + -29x + 4x2

Add '-4x2' to each side of the equation.
5 + 4x2 + -4x2 = 64 + -29x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + 0 = 64 + -29x + 4x2 + -4x2
5 = 64 + -29x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 = 64 + -29x + 0
5 = 64 + -29x

Solving
5 = 64 + -29x

Solving for variable 'x'.

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

Add '29x' to each side of the equation.
5 + 29x = 64 + -29x + 29x

Combine like terms: -29x + 29x = 0
5 + 29x = 64 + 0
5 + 29x = 64

Add '-5' to each side of the equation.
5 + -5 + 29x = 64 + -5

Combine like terms: 5 + -5 = 0
0 + 29x = 64 + -5
29x = 64 + -5

Combine like terms: 64 + -5 = 59
29x = 59

Divide each side by '29'.
x = 2.034482759

Simplifying
x = 2.034482759

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