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Simplifying 3(x + 1)(3x + -1) = 0 Reorder the terms: 3(1 + x)(3x + -1) = 0 Reorder the terms: 3(1 + x)(-1 + 3x) = 0 Multiply (1 + x) * (-1 + 3x) 3(1(-1 + 3x) + x(-1 + 3x)) = 0 3((-1 * 1 + 3x * 1) + x(-1 + 3x)) = 0 3((-1 + 3x) + x(-1 + 3x)) = 0 3(-1 + 3x + (-1 * x + 3x * x)) = 0 3(-1 + 3x + (-1x + 3x2)) = 0 Combine like terms: 3x + -1x = 2x 3(-1 + 2x + 3x2) = 0 (-1 * 3 + 2x * 3 + 3x2 * 3) = 0 (-3 + 6x + 9x2) = 0 Solving -3 + 6x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 2x + 3x2) = 0 Factor a trinomial. 3((-1 + -1x)(1 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-1, 0.3333333333}
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