5x-2+2*(2x+1)*(2x+1)=6x

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Solution for 5x-2+2*(2x+1)*(2x+1)=6x equation:


Simplifying
5x + -2 + 2(2x + 1)(2x + 1) = 6x

Reorder the terms:
5x + -2 + 2(1 + 2x)(2x + 1) = 6x

Reorder the terms:
5x + -2 + 2(1 + 2x)(1 + 2x) = 6x

Multiply (1 + 2x) * (1 + 2x)
5x + -2 + 2(1(1 + 2x) + 2x * (1 + 2x)) = 6x
5x + -2 + 2((1 * 1 + 2x * 1) + 2x * (1 + 2x)) = 6x
5x + -2 + 2((1 + 2x) + 2x * (1 + 2x)) = 6x
5x + -2 + 2(1 + 2x + (1 * 2x + 2x * 2x)) = 6x
5x + -2 + 2(1 + 2x + (2x + 4x2)) = 6x

Combine like terms: 2x + 2x = 4x
5x + -2 + 2(1 + 4x + 4x2) = 6x
5x + -2 + (1 * 2 + 4x * 2 + 4x2 * 2) = 6x
5x + -2 + (2 + 8x + 8x2) = 6x

Reorder the terms:
-2 + 2 + 5x + 8x + 8x2 = 6x

Combine like terms: -2 + 2 = 0
0 + 5x + 8x + 8x2 = 6x
5x + 8x + 8x2 = 6x

Combine like terms: 5x + 8x = 13x
13x + 8x2 = 6x

Solving
13x + 8x2 = 6x

Solving for variable 'x'.

Reorder the terms:
13x + -6x + 8x2 = 6x + -6x

Combine like terms: 13x + -6x = 7x
7x + 8x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
7x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 8x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + 8x)' equal to zero and attempt to solve:

Simplifying
7 + 8x = 0

Solving
7 + 8x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8x = 0 + -7
8x = 0 + -7

Combine like terms: 0 + -7 = -7
8x = -7

Divide each side by '8'.
x = -0.875

Simplifying
x = -0.875
Solution
x = {0, -0.875}

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