(3x-9)(4x+8)=0

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Solution for (3x-9)(4x+8)=0 equation:


Simplifying
(3x + -9)(4x + 8) = 0

Reorder the terms:
(-9 + 3x)(4x + 8) = 0

Reorder the terms:
(-9 + 3x)(8 + 4x) = 0

Multiply (-9 + 3x) * (8 + 4x)
(-9(8 + 4x) + 3x * (8 + 4x)) = 0
((8 * -9 + 4x * -9) + 3x * (8 + 4x)) = 0
((-72 + -36x) + 3x * (8 + 4x)) = 0
(-72 + -36x + (8 * 3x + 4x * 3x)) = 0
(-72 + -36x + (24x + 12x2)) = 0

Combine like terms: -36x + 24x = -12x
(-72 + -12x + 12x2) = 0

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

Solving for variable 'x'.

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

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

Ignore the factor 12.

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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