12(2x+3)(x-2)=0

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Solution for 12(2x+3)(x-2)=0 equation:


Simplifying
12(2x + 3)(x + -2) = 0

Reorder the terms:
12(3 + 2x)(x + -2) = 0

Reorder the terms:
12(3 + 2x)(-2 + x) = 0

Multiply (3 + 2x) * (-2 + x)
12(3(-2 + x) + 2x * (-2 + x)) = 0
12((-2 * 3 + x * 3) + 2x * (-2 + x)) = 0
12((-6 + 3x) + 2x * (-2 + x)) = 0
12(-6 + 3x + (-2 * 2x + x * 2x)) = 0
12(-6 + 3x + (-4x + 2x2)) = 0

Combine like terms: 3x + -4x = -1x
12(-6 + -1x + 2x2) = 0
(-6 * 12 + -1x * 12 + 2x2 * 12) = 0
(-72 + -12x + 24x2) = 0

Solving
-72 + -12x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-6 + -1x + 2x2) = 0

Factor a trinomial.
12((-3 + -2x)(2 + -1x)) = 0

Ignore the factor 12.

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

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 = {-1.5, 2}

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