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Simplifying 0 = (10x * x * x) + -1(15x * x) Multiply x * x 0 = (10x2 * x) + -1(15x * x) Multiply x2 * x 0 = (10x3) + -1(15x * x) Multiply x * x 0 = (10x3) + -1(15x2) Remove parenthesis around (15x2) 0 = (10x3) + -1 * 15x2 Multiply -1 * 15 0 = (10x3) + -15x2 Reorder the terms: 0 = -15x2 + (10x3) Solving 0 = -15x2 + (10x3) Solving for variable 'x'. Remove the zero: 15x2 + (-10x3) = -15x2 + (10x3) + 15x2 + (-10x3) Reorder the terms: 15x2 + (-10x3) = -15x2 + 15x2 + (10x3) + (-10x3) Combine like terms: -15x2 + 15x2 = 0 15x2 + (-10x3) = 0 + (10x3) + (-10x3) 15x2 + (-10x3) = (10x3) + (-10x3) Combine like terms: (10x3) + (-10x3) = 0 15x2 + (-10x3) = 0 Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(3 + (-2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 = 1.5Solution
x = {0, 1.5}
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