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Simplifying 0 = (18x + 24)(x + -12) Reorder the terms: 0 = (24 + 18x)(x + -12) Reorder the terms: 0 = (24 + 18x)(-12 + x) Multiply (24 + 18x) * (-12 + x) 0 = (24(-12 + x) + 18x * (-12 + x)) 0 = ((-12 * 24 + x * 24) + 18x * (-12 + x)) 0 = ((-288 + 24x) + 18x * (-12 + x)) 0 = (-288 + 24x + (-12 * 18x + x * 18x)) 0 = (-288 + 24x + (-216x + 18x2)) Combine like terms: 24x + -216x = -192x 0 = (-288 + -192x + 18x2) Solving 0 = -288 + -192x + 18x2 Solving for variable 'x'. Combine like terms: 0 + 288 = 288 288 + 192x + -18x2 = -288 + -192x + 18x2 + 288 + 192x + -18x2 Reorder the terms: 288 + 192x + -18x2 = -288 + 288 + -192x + 192x + 18x2 + -18x2 Combine like terms: -288 + 288 = 0 288 + 192x + -18x2 = 0 + -192x + 192x + 18x2 + -18x2 288 + 192x + -18x2 = -192x + 192x + 18x2 + -18x2 Combine like terms: -192x + 192x = 0 288 + 192x + -18x2 = 0 + 18x2 + -18x2 288 + 192x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 288 + 192x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(48 + 32x + -3x2) = 0 Factor a trinomial. 6((12 + -1x)(4 + 3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {12, -1.333333333}
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