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Simplifying 0 = (6x2 + 3x + -3) Reorder the terms: 0 = (-3 + 3x + 6x2) Remove parenthesis around (-3 + 3x + 6x2) 0 = -3 + 3x + 6x2 Solving 0 = -3 + 3x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + -3x + -6x2 = -3 + 3x + 6x2 + 3 + -3x + -6x2 Reorder the terms: 3 + -3x + -6x2 = -3 + 3 + 3x + -3x + 6x2 + -6x2 Combine like terms: -3 + 3 = 0 3 + -3x + -6x2 = 0 + 3x + -3x + 6x2 + -6x2 3 + -3x + -6x2 = 3x + -3x + 6x2 + -6x2 Combine like terms: 3x + -3x = 0 3 + -3x + -6x2 = 0 + 6x2 + -6x2 3 + -3x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + -3x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -1x + -2x2) = 0 Factor a trinomial. 3((1 + -2x)(1 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0.5, -1}
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