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Simplifying 0 = 3x2 + 17x + 20 Reorder the terms: 0 = 20 + 17x + 3x2 Solving 0 = 20 + 17x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -17x + -3x2 = 20 + 17x + 3x2 + -20 + -17x + -3x2 Reorder the terms: -20 + -17x + -3x2 = 20 + -20 + 17x + -17x + 3x2 + -3x2 Combine like terms: 20 + -20 = 0 -20 + -17x + -3x2 = 0 + 17x + -17x + 3x2 + -3x2 -20 + -17x + -3x2 = 17x + -17x + 3x2 + -3x2 Combine like terms: 17x + -17x = 0 -20 + -17x + -3x2 = 0 + 3x2 + -3x2 -20 + -17x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -20 + -17x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 17x + 3x2) = 0 Factor a trinomial. -1((4 + x)(5 + 3x)) = 0 Ignore the factor -1.Subproblem 1
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 = -4Subproblem 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 = {-4, -1.666666667}
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