12x(3x-2)+(3x-2)=0

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Solution for 12x(3x-2)+(3x-2)=0 equation: 


Simplifying
12x(3x + -2) + (3x + -2) = 0

Reorder the terms:
12x(-2 + 3x) + (3x + -2) = 0
(-2 * 12x + 3x * 12x) + (3x + -2) = 0
(-24x + 36x2) + (3x + -2) = 0

Reorder the terms:
-24x + 36x2 + (-2 + 3x) = 0

Remove parenthesis around (-2 + 3x)
-24x + 36x2 + -2 + 3x = 0

Reorder the terms:
-2 + -24x + 3x + 36x2 = 0

Combine like terms: -24x + 3x = -21x
-2 + -21x + 36x2 = 0

Solving
-2 + -21x + 36x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -12x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -12x)' equal to zero and attempt to solve:

Simplifying
-1 + -12x = 0

Solving
-1 + -12x = 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 + -12x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -12x = 0 + 1
-12x = 0 + 1

Combine like terms: 0 + 1 = 1
-12x = 1

Divide each side by '-12'.
x = -0.08333333333

Simplifying
x = -0.08333333333

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.08333333333, 0.6666666667}

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