(-6x+3)(3x+2)=0

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Solution for (-6x+3)(3x+2)=0 equation: 


Simplifying
(-6x + 3)(3x + 2) = 0

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

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

Multiply (3 + -6x) * (2 + 3x)
(3(2 + 3x) + -6x * (2 + 3x)) = 0
((2 * 3 + 3x * 3) + -6x * (2 + 3x)) = 0
((6 + 9x) + -6x * (2 + 3x)) = 0
(6 + 9x + (2 * -6x + 3x * -6x)) = 0
(6 + 9x + (-12x + -18x2)) = 0

Combine like terms: 9x + -12x = -3x
(6 + -3x + -18x2) = 0

Solving
6 + -3x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1x + -6x2) = 0

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

Ignore the factor 3.

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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 = {0.5, -0.6666666667}

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