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

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


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

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

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

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

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

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

Remove parenthesis around (-2 + 6x)
-2 + -1x + 6x2 = -2 + 6x

Add '2' to each side of the equation.
-2 + -1x + 2 + 6x2 = -2 + 2 + 6x

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

Combine like terms: -2 + 2 = 0
0 + -1x + 6x2 = -2 + 2 + 6x
-1x + 6x2 = -2 + 2 + 6x

Combine like terms: -2 + 2 = 0
-1x + 6x2 = 0 + 6x
-1x + 6x2 = 6x

Solving
-1x + 6x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-1x + -6x + 6x2 = 6x + -6x

Combine like terms: -1x + -6x = -7x
-7x + 6x2 = 6x + -6x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 6x) = 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 + 6x)' equal to zero and attempt to solve:

Simplifying
-7 + 6x = 0

Solving
-7 + 6x = 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 + 6x = 0 + 7

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

Combine like terms: 0 + 7 = 7
6x = 7

Divide each side by '6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0, 1.166666667}

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