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Simplifying (2x + -1)(3x2 + -1x) = 0 Reorder the terms: (-1 + 2x)(3x2 + -1x) = 0 Reorder the terms: (-1 + 2x)(-1x + 3x2) = 0 Multiply (-1 + 2x) * (-1x + 3x2) (-1(-1x + 3x2) + 2x * (-1x + 3x2)) = 0 ((-1x * -1 + 3x2 * -1) + 2x * (-1x + 3x2)) = 0 ((1x + -3x2) + 2x * (-1x + 3x2)) = 0 (1x + -3x2 + (-1x * 2x + 3x2 * 2x)) = 0 (1x + -3x2 + (-2x2 + 6x3)) = 0 Combine like terms: -3x2 + -2x2 = -5x2 (1x + -5x2 + 6x3) = 0 Solving 1x + -5x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -5x + 6x2) = 0 Factor a trinomial. x((1 + -3x)(1 + -2x)) = 0Subproblem 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 '(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 = 0.3333333333Subproblem 3
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, 0.3333333333, 0.5}
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