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Simplifying 0 = 3(3x2 + 5x + 2) Reorder the terms: 0 = 3(2 + 5x + 3x2) 0 = (2 * 3 + 5x * 3 + 3x2 * 3) 0 = (6 + 15x + 9x2) Solving 0 = 6 + 15x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -15x + -9x2 = 6 + 15x + 9x2 + -6 + -15x + -9x2 Reorder the terms: -6 + -15x + -9x2 = 6 + -6 + 15x + -15x + 9x2 + -9x2 Combine like terms: 6 + -6 = 0 -6 + -15x + -9x2 = 0 + 15x + -15x + 9x2 + -9x2 -6 + -15x + -9x2 = 15x + -15x + 9x2 + -9x2 Combine like terms: 15x + -15x = 0 -6 + -15x + -9x2 = 0 + 9x2 + -9x2 -6 + -15x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -6 + -15x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(2 + 5x + 3x2) = 0 Factor a trinomial. -3((1 + x)(2 + 3x)) = 0 Ignore the factor -3.Subproblem 1
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 = -1Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-1, -0.6666666667}
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