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

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


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

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

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

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

Combine like terms: 2x + -3x = -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 + -1x + x2) = 0

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

Ignore the factor 6.

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 '(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

Solution

x = {-2, 3}

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