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

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


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

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

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

Multiply (-2 + x) * (2 + 3x)
(-2(2 + 3x) + x(2 + 3x)) = 0
((2 * -2 + 3x * -2) + x(2 + 3x)) = 0
((-4 + -6x) + x(2 + 3x)) = 0
(-4 + -6x + (2 * x + 3x * x)) = 0
(-4 + -6x + (2x + 3x2)) = 0

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

Solving
-4 + -4x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-0.6666666667, 2}

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