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Simplifying (10x2 + (-20x))(-30x + 60) = 0 Reorder the terms: ((-20x) + 10x2)(-30x + 60) = 0 Reorder the terms: ((-20x) + 10x2)(60 + -30x) = 0 Multiply ((-20x) + 10x2) * (60 + -30x) ((-20x)(60 + -30x) + 10x2 * (60 + -30x)) = 0 ((60 * -20x + -30x * -20x) + 10x2 * (60 + -30x)) = 0 ((-1200x + 600x2) + 10x2 * (60 + -30x)) = 0 (-1200x + 600x2 + (60 * 10x2 + -30x * 10x2)) = 0 (-1200x + 600x2 + (600x2 + -300x3)) = 0 Combine like terms: 600x2 + 600x2 = 1200x2 (-1200x + 1200x2 + -300x3) = 0 Solving -1200x + 1200x2 + -300x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '300x'. 300x(-4 + 4x + -1x2) = 0 Factor a trinomial. 300x((-2 + x)(2 + -1x)) = 0 Ignore the factor 300.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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, 2, 2}
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