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Simplifying 0 = 12x2 + -184x + 480 Reorder the terms: 0 = 480 + -184x + 12x2 Solving 0 = 480 + -184x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -480 = -480 -480 + 184x + -12x2 = 480 + -184x + 12x2 + -480 + 184x + -12x2 Reorder the terms: -480 + 184x + -12x2 = 480 + -480 + -184x + 184x + 12x2 + -12x2 Combine like terms: 480 + -480 = 0 -480 + 184x + -12x2 = 0 + -184x + 184x + 12x2 + -12x2 -480 + 184x + -12x2 = -184x + 184x + 12x2 + -12x2 Combine like terms: -184x + 184x = 0 -480 + 184x + -12x2 = 0 + 12x2 + -12x2 -480 + 184x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -480 + 184x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-120 + 46x + -3x2) = 0 Factor a trinomial. 4((-12 + x)(10 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 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 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
Set the factor '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Divide each side by '-3'. x = 3.333333333 Simplifying x = 3.333333333Solution
x = {12, 3.333333333}
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