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Simplifying 460 = -5(x + 3)(x + -24) Reorder the terms: 460 = -5(3 + x)(x + -24) Reorder the terms: 460 = -5(3 + x)(-24 + x) Multiply (3 + x) * (-24 + x) 460 = -5(3(-24 + x) + x(-24 + x)) 460 = -5((-24 * 3 + x * 3) + x(-24 + x)) 460 = -5((-72 + 3x) + x(-24 + x)) 460 = -5(-72 + 3x + (-24 * x + x * x)) 460 = -5(-72 + 3x + (-24x + x2)) Combine like terms: 3x + -24x = -21x 460 = -5(-72 + -21x + x2) 460 = (-72 * -5 + -21x * -5 + x2 * -5) 460 = (360 + 105x + -5x2) Solving 460 = 360 + 105x + -5x2 Solving for variable 'x'. Combine like terms: 460 + -360 = 100 100 + -105x + 5x2 = 360 + 105x + -5x2 + -360 + -105x + 5x2 Reorder the terms: 100 + -105x + 5x2 = 360 + -360 + 105x + -105x + -5x2 + 5x2 Combine like terms: 360 + -360 = 0 100 + -105x + 5x2 = 0 + 105x + -105x + -5x2 + 5x2 100 + -105x + 5x2 = 105x + -105x + -5x2 + 5x2 Combine like terms: 105x + -105x = 0 100 + -105x + 5x2 = 0 + -5x2 + 5x2 100 + -105x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 100 + -105x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(20 + -21x + x2) = 0 Factor a trinomial. 5((1 + -1x)(20 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {1, 20}
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