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Simplifying 0 = 6x2 + 23x + 20 Reorder the terms: 0 = 20 + 23x + 6x2 Solving 0 = 20 + 23x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -23x + -6x2 = 20 + 23x + 6x2 + -20 + -23x + -6x2 Reorder the terms: -20 + -23x + -6x2 = 20 + -20 + 23x + -23x + 6x2 + -6x2 Combine like terms: 20 + -20 = 0 -20 + -23x + -6x2 = 0 + 23x + -23x + 6x2 + -6x2 -20 + -23x + -6x2 = 23x + -23x + 6x2 + -6x2 Combine like terms: 23x + -23x = 0 -20 + -23x + -6x2 = 0 + 6x2 + -6x2 -20 + -23x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -20 + -23x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 23x + 6x2) = 0 Factor a trinomial. -1((5 + 2x)(4 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-2.5, -1.333333333}
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