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Simplifying 0 = 3x2 + 24x + 45 Reorder the terms: 0 = 45 + 24x + 3x2 Solving 0 = 45 + 24x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + -24x + -3x2 = 45 + 24x + 3x2 + -45 + -24x + -3x2 Reorder the terms: -45 + -24x + -3x2 = 45 + -45 + 24x + -24x + 3x2 + -3x2 Combine like terms: 45 + -45 = 0 -45 + -24x + -3x2 = 0 + 24x + -24x + 3x2 + -3x2 -45 + -24x + -3x2 = 24x + -24x + 3x2 + -3x2 Combine like terms: 24x + -24x = 0 -45 + -24x + -3x2 = 0 + 3x2 + -3x2 -45 + -24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -45 + -24x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(15 + 8x + x2) = 0 Factor a trinomial. -3((5 + x)(3 + x)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-5, -3}
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