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Simplifying x3 + 4(x3 + -10) = 20(3x + -1x2 + -2) Reorder the terms: x3 + 4(-10 + x3) = 20(3x + -1x2 + -2) x3 + (-10 * 4 + x3 * 4) = 20(3x + -1x2 + -2) x3 + (-40 + 4x3) = 20(3x + -1x2 + -2) Reorder the terms: -40 + x3 + 4x3 = 20(3x + -1x2 + -2) Combine like terms: x3 + 4x3 = 5x3 -40 + 5x3 = 20(3x + -1x2 + -2) Reorder the terms: -40 + 5x3 = 20(-2 + 3x + -1x2) -40 + 5x3 = (-2 * 20 + 3x * 20 + -1x2 * 20) -40 + 5x3 = (-40 + 60x + -20x2) Add '40' to each side of the equation. -40 + 40 + 5x3 = -40 + 60x + 40 + -20x2 Combine like terms: -40 + 40 = 0 0 + 5x3 = -40 + 60x + 40 + -20x2 5x3 = -40 + 60x + 40 + -20x2 Reorder the terms: 5x3 = -40 + 40 + 60x + -20x2 Combine like terms: -40 + 40 = 0 5x3 = 0 + 60x + -20x2 5x3 = 60x + -20x2 Solving 5x3 = 60x + -20x2 Solving for variable 'x'. Reorder the terms: -60x + 20x2 + 5x3 = 60x + -20x2 + -60x + 20x2 Reorder the terms: -60x + 20x2 + 5x3 = 60x + -60x + -20x2 + 20x2 Combine like terms: 60x + -60x = 0 -60x + 20x2 + 5x3 = 0 + -20x2 + 20x2 -60x + 20x2 + 5x3 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 -60x + 20x2 + 5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-12 + 4x + x2) = 0 Factor a trinomial. 5x((-6 + -1x)(2 + -1x)) = 0 Ignore the factor 5.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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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, -6, 2}
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