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Simplifying 2x(9x + -1)(2x + 3) = 0 Reorder the terms: 2x(-1 + 9x)(2x + 3) = 0 Reorder the terms: 2x(-1 + 9x)(3 + 2x) = 0 Multiply (-1 + 9x) * (3 + 2x) 2x(-1(3 + 2x) + 9x * (3 + 2x)) = 0 2x((3 * -1 + 2x * -1) + 9x * (3 + 2x)) = 0 2x((-3 + -2x) + 9x * (3 + 2x)) = 0 2x(-3 + -2x + (3 * 9x + 2x * 9x)) = 0 2x(-3 + -2x + (27x + 18x2)) = 0 Combine like terms: -2x + 27x = 25x 2x(-3 + 25x + 18x2) = 0 (-3 * 2x + 25x * 2x + 18x2 * 2x) = 0 (-6x + 50x2 + 36x3) = 0 Solving -6x + 50x2 + 36x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-3 + 25x + 18x2) = 0 Factor a trinomial. 2x((-3 + -2x)(1 + -9x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 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 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111Solution
x = {0, -1.5, 0.1111111111}
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