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Simplifying (2x + 3)(10x)(3x + -1) = 0 Reorder the terms: (3 + 2x)(10x)(3x + -1) = 0 Remove parenthesis around (10x) (3 + 2x) * 10x(3x + -1) = 0 Reorder the terms: (3 + 2x) * 10x(-1 + 3x) = 0 Reorder the terms for easier multiplication: 10x(3 + 2x)(-1 + 3x) = 0 Multiply (3 + 2x) * (-1 + 3x) 10x(3(-1 + 3x) + 2x * (-1 + 3x)) = 0 10x((-1 * 3 + 3x * 3) + 2x * (-1 + 3x)) = 0 10x((-3 + 9x) + 2x * (-1 + 3x)) = 0 10x(-3 + 9x + (-1 * 2x + 3x * 2x)) = 0 10x(-3 + 9x + (-2x + 6x2)) = 0 Combine like terms: 9x + -2x = 7x 10x(-3 + 7x + 6x2) = 0 (-3 * 10x + 7x * 10x + 6x2 * 10x) = 0 (-30x + 70x2 + 60x3) = 0 Solving -30x + 70x2 + 60x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(-3 + 7x + 6x2) = 0 Factor a trinomial. 10x((-3 + -2x)(1 + -3x)) = 0 Ignore the factor 10.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 + -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, -1.5, 0.3333333333}
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