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Simplifying 0 = 12x2 + 42x + -24 Reorder the terms: 0 = -24 + 42x + 12x2 Solving 0 = -24 + 42x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + -42x + -12x2 = -24 + 42x + 12x2 + 24 + -42x + -12x2 Reorder the terms: 24 + -42x + -12x2 = -24 + 24 + 42x + -42x + 12x2 + -12x2 Combine like terms: -24 + 24 = 0 24 + -42x + -12x2 = 0 + 42x + -42x + 12x2 + -12x2 24 + -42x + -12x2 = 42x + -42x + 12x2 + -12x2 Combine like terms: 42x + -42x = 0 24 + -42x + -12x2 = 0 + 12x2 + -12x2 24 + -42x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 24 + -42x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(4 + -7x + -2x2) = 0 Factor a trinomial. 6((1 + -2x)(4 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {0.5, -4}
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