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Simplifying 3x(2x + -5)(3x + -2) = 0 Reorder the terms: 3x(-5 + 2x)(3x + -2) = 0 Reorder the terms: 3x(-5 + 2x)(-2 + 3x) = 0 Multiply (-5 + 2x) * (-2 + 3x) 3x(-5(-2 + 3x) + 2x * (-2 + 3x)) = 0 3x((-2 * -5 + 3x * -5) + 2x * (-2 + 3x)) = 0 3x((10 + -15x) + 2x * (-2 + 3x)) = 0 3x(10 + -15x + (-2 * 2x + 3x * 2x)) = 0 3x(10 + -15x + (-4x + 6x2)) = 0 Combine like terms: -15x + -4x = -19x 3x(10 + -19x + 6x2) = 0 (10 * 3x + -19x * 3x + 6x2 * 3x) = 0 (30x + -57x2 + 18x3) = 0 Solving 30x + -57x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(10 + -19x + 6x2) = 0 Factor a trinomial. 3x((2 + -3x)(5 + -2x)) = 0 Ignore the factor 3.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 '(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 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, 0.6666666667, 2.5}
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