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Simplifying 0 = 12x2 + -88x + 96 Reorder the terms: 0 = 96 + -88x + 12x2 Solving 0 = 96 + -88x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -96 = -96 -96 + 88x + -12x2 = 96 + -88x + 12x2 + -96 + 88x + -12x2 Reorder the terms: -96 + 88x + -12x2 = 96 + -96 + -88x + 88x + 12x2 + -12x2 Combine like terms: 96 + -96 = 0 -96 + 88x + -12x2 = 0 + -88x + 88x + 12x2 + -12x2 -96 + 88x + -12x2 = -88x + 88x + 12x2 + -12x2 Combine like terms: -88x + 88x = 0 -96 + 88x + -12x2 = 0 + 12x2 + -12x2 -96 + 88x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -96 + 88x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + 22x + -3x2) = 0 Factor a trinomial. 4((-6 + x)(4 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 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 = {6, 1.333333333}
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