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Simplifying (9x + 3)(-4x + -2) = 0 Reorder the terms: (3 + 9x)(-4x + -2) = 0 Reorder the terms: (3 + 9x)(-2 + -4x) = 0 Multiply (3 + 9x) * (-2 + -4x) (3(-2 + -4x) + 9x * (-2 + -4x)) = 0 ((-2 * 3 + -4x * 3) + 9x * (-2 + -4x)) = 0 ((-6 + -12x) + 9x * (-2 + -4x)) = 0 (-6 + -12x + (-2 * 9x + -4x * 9x)) = 0 (-6 + -12x + (-18x + -36x2)) = 0 Combine like terms: -12x + -18x = -30x (-6 + -30x + -36x2) = 0 Solving -6 + -30x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(1 + 5x + 6x2) = 0 Factor a trinomial. -6((1 + 2x)(1 + 3x)) = 0 Ignore the factor -6.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 + 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 = {-0.5, -0.3333333333}
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