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Simplifying 0 = 6x2 + 23x + 15 Reorder the terms: 0 = 15 + 23x + 6x2 Solving 0 = 15 + 23x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + -23x + -6x2 = 15 + 23x + 6x2 + -15 + -23x + -6x2 Reorder the terms: -15 + -23x + -6x2 = 15 + -15 + 23x + -23x + 6x2 + -6x2 Combine like terms: 15 + -15 = 0 -15 + -23x + -6x2 = 0 + 23x + -23x + 6x2 + -6x2 -15 + -23x + -6x2 = 23x + -23x + 6x2 + -6x2 Combine like terms: 23x + -23x = 0 -15 + -23x + -6x2 = 0 + 6x2 + -6x2 -15 + -23x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -15 + -23x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 23x + 6x2) = 0 Factor a trinomial. -1((3 + x)(5 + 6x)) = 0 Ignore the factor -1.Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve: Simplifying 5 + 6x = 0 Solving 5 + 6x = 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 + 6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6x = 0 + -5 6x = 0 + -5 Combine like terms: 0 + -5 = -5 6x = -5 Divide each side by '6'. x = -0.8333333333 Simplifying x = -0.8333333333Solution
x = {-3, -0.8333333333}
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