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

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


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

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

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

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

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

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

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

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

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

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

Solving
2 + -4x + 6x2 = 6 + 6x

Solving for variable 'x'.

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

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

Combine like terms: -4x + -6x = -10x
-4 + -10x + 6x2 = 6 + 6x + -6 + -6x

Reorder the terms:
-4 + -10x + 6x2 = 6 + -6 + 6x + -6x

Combine like terms: 6 + -6 = 0
-4 + -10x + 6x2 = 0 + 6x + -6x
-4 + -10x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-4 + -10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5x + 3x2) = 0

Factor a trinomial.
2((-1 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.3333333333, 2}

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