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

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


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

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

Reorder the terms:
-2x + 3x2 + 2(-2 + 3x) = 0
-2x + 3x2 + (-2 * 2 + 3x * 2) = 0
-2x + 3x2 + (-4 + 6x) = 0

Reorder the terms:
-4 + -2x + 6x + 3x2 = 0

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

Solving
-4 + 4x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-2, 0.6666666667}

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