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Simplifying 24x2 + -4x + -54 = 6 Reorder the terms: -54 + -4x + 24x2 = 6 Solving -54 + -4x + 24x2 = 6 Solving for variable 'x'. Reorder the terms: -54 + -6 + -4x + 24x2 = 6 + -6 Combine like terms: -54 + -6 = -60 -60 + -4x + 24x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -60 + -4x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -1x + 6x2) = 0 Factor a trinomial. 4((-3 + -2x)(5 + -3x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {-1.5, 1.666666667}
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