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Simplifying (x * 2 + -9)(x + -5) * x = 0 Reorder the terms for easier multiplication: (2x + -9)(x + -5) * x = 0 Reorder the terms: (-9 + 2x)(x + -5) * x = 0 Reorder the terms: (-9 + 2x)(-5 + x) * x = 0 Reorder the terms for easier multiplication: x(-9 + 2x)(-5 + x) = 0 Multiply (-9 + 2x) * (-5 + x) x(-9(-5 + x) + 2x * (-5 + x)) = 0 x((-5 * -9 + x * -9) + 2x * (-5 + x)) = 0 x((45 + -9x) + 2x * (-5 + x)) = 0 x(45 + -9x + (-5 * 2x + x * 2x)) = 0 x(45 + -9x + (-10x + 2x2)) = 0 Combine like terms: -9x + -10x = -19x x(45 + -19x + 2x2) = 0 (45 * x + -19x * x + 2x2 * x) = 0 (45x + -19x2 + 2x3) = 0 Solving 45x + -19x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(45 + -19x + 2x2) = 0 Factor a trinomial. x((9 + -2x)(5 + -1x)) = 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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, 4.5, 5}
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