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Simplifying -5x(x + 3)(-2x + -17) = 0 Reorder the terms: -5x(3 + x)(-2x + -17) = 0 Reorder the terms: -5x(3 + x)(-17 + -2x) = 0 Multiply (3 + x) * (-17 + -2x) -5x(3(-17 + -2x) + x(-17 + -2x)) = 0 -5x((-17 * 3 + -2x * 3) + x(-17 + -2x)) = 0 -5x((-51 + -6x) + x(-17 + -2x)) = 0 -5x(-51 + -6x + (-17 * x + -2x * x)) = 0 -5x(-51 + -6x + (-17x + -2x2)) = 0 Combine like terms: -6x + -17x = -23x -5x(-51 + -23x + -2x2) = 0 (-51 * -5x + -23x * -5x + -2x2 * -5x) = 0 (255x + 115x2 + 10x3) = 0 Solving 255x + 115x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(51 + 23x + 2x2) = 0 Factor a trinomial. 5x((17 + 2x)(3 + x)) = 0 Ignore the factor 5.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 '(17 + 2x)' equal to zero and attempt to solve: Simplifying 17 + 2x = 0 Solving 17 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 2x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 2x = 0 + -17 2x = 0 + -17 Combine like terms: 0 + -17 = -17 2x = -17 Divide each side by '2'. x = -8.5 Simplifying x = -8.5Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -8.5, -3}
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