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Simplifying x(29 + -2x)(16 + -2x) = 0 Multiply (29 + -2x) * (16 + -2x) x(29(16 + -2x) + -2x * (16 + -2x)) = 0 x((16 * 29 + -2x * 29) + -2x * (16 + -2x)) = 0 x((464 + -58x) + -2x * (16 + -2x)) = 0 x(464 + -58x + (16 * -2x + -2x * -2x)) = 0 x(464 + -58x + (-32x + 4x2)) = 0 Combine like terms: -58x + -32x = -90x x(464 + -90x + 4x2) = 0 (464 * x + -90x * x + 4x2 * x) = 0 (464x + -90x2 + 4x3) = 0 Solving 464x + -90x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(232 + -45x + 2x2) = 0 Factor a trinomial. 2x((8 + -1x)(29 + -2x)) = 0 Ignore the factor 2.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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 3
Set the factor '(29 + -2x)' equal to zero and attempt to solve: Simplifying 29 + -2x = 0 Solving 29 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -2x = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -2x = 0 + -29 -2x = 0 + -29 Combine like terms: 0 + -29 = -29 -2x = -29 Divide each side by '-2'. x = 14.5 Simplifying x = 14.5Solution
x = {0, 8, 14.5}
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