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Simplifying (6x + -3)(3x + 2) = 0 Reorder the terms: (-3 + 6x)(3x + 2) = 0 Reorder the terms: (-3 + 6x)(2 + 3x) = 0 Multiply (-3 + 6x) * (2 + 3x) (-3(2 + 3x) + 6x * (2 + 3x)) = 0 ((2 * -3 + 3x * -3) + 6x * (2 + 3x)) = 0 ((-6 + -9x) + 6x * (2 + 3x)) = 0 (-6 + -9x + (2 * 6x + 3x * 6x)) = 0 (-6 + -9x + (12x + 18x2)) = 0 Combine like terms: -9x + 12x = 3x (-6 + 3x + 18x2) = 0 Solving -6 + 3x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + x + 6x2) = 0 Factor a trinomial. 3((-2 + -3x)(1 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -0.6666666667Subproblem 2
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 = 0.5Solution
x = {-0.6666666667, 0.5}
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