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Simplifying 0 = 6x2 + 9x + -27 Reorder the terms: 0 = -27 + 9x + 6x2 Solving 0 = -27 + 9x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 27 = 27 27 + -9x + -6x2 = -27 + 9x + 6x2 + 27 + -9x + -6x2 Reorder the terms: 27 + -9x + -6x2 = -27 + 27 + 9x + -9x + 6x2 + -6x2 Combine like terms: -27 + 27 = 0 27 + -9x + -6x2 = 0 + 9x + -9x + 6x2 + -6x2 27 + -9x + -6x2 = 9x + -9x + 6x2 + -6x2 Combine like terms: 9x + -9x = 0 27 + -9x + -6x2 = 0 + 6x2 + -6x2 27 + -9x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 27 + -9x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -3x + -2x2) = 0 Factor a trinomial. 3((3 + -2x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 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 = {1.5, -3}
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