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Simplifying (3x + -12)(-2x + 10) = 0 Reorder the terms: (-12 + 3x)(-2x + 10) = 0 Reorder the terms: (-12 + 3x)(10 + -2x) = 0 Multiply (-12 + 3x) * (10 + -2x) (-12(10 + -2x) + 3x * (10 + -2x)) = 0 ((10 * -12 + -2x * -12) + 3x * (10 + -2x)) = 0 ((-120 + 24x) + 3x * (10 + -2x)) = 0 (-120 + 24x + (10 * 3x + -2x * 3x)) = 0 (-120 + 24x + (30x + -6x2)) = 0 Combine like terms: 24x + 30x = 54x (-120 + 54x + -6x2) = 0 Solving -120 + 54x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + 9x + -1x2) = 0 Factor a trinomial. 6((-5 + x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {5, 4}
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