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Simplifying (41 + -2x)(24 + -2x) * x = 0 Reorder the terms for easier multiplication: x(41 + -2x)(24 + -2x) = 0 Multiply (41 + -2x) * (24 + -2x) x(41(24 + -2x) + -2x * (24 + -2x)) = 0 x((24 * 41 + -2x * 41) + -2x * (24 + -2x)) = 0 x((984 + -82x) + -2x * (24 + -2x)) = 0 x(984 + -82x + (24 * -2x + -2x * -2x)) = 0 x(984 + -82x + (-48x + 4x2)) = 0 Combine like terms: -82x + -48x = -130x x(984 + -130x + 4x2) = 0 (984 * x + -130x * x + 4x2 * x) = 0 (984x + -130x2 + 4x3) = 0 Solving 984x + -130x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(492 + -65x + 2x2) = 0 Factor a trinomial. 2x((12 + -1x)(41 + -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 '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 3
Set the factor '(41 + -2x)' equal to zero and attempt to solve: Simplifying 41 + -2x = 0 Solving 41 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + -2x = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -2x = 0 + -41 -2x = 0 + -41 Combine like terms: 0 + -41 = -41 -2x = -41 Divide each side by '-2'. x = 20.5 Simplifying x = 20.5Solution
x = {0, 12, 20.5}
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