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

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


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

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

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

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

Combine like terms: 3x + -2x = 1x
6(-6 + 1x + x2) = 0
(-6 * 6 + 1x * 6 + x2 * 6) = 0
(-36 + 6x + 6x2) = 0

Solving
-36 + 6x + 6x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
6((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 2}

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