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Simplifying x3 = 13x2 + -42x Reorder the terms: x3 = -42x + 13x2 Solving x3 = -42x + 13x2 Solving for variable 'x'. Reorder the terms: 42x + -13x2 + x3 = -42x + 13x2 + 42x + -13x2 Reorder the terms: 42x + -13x2 + x3 = -42x + 42x + 13x2 + -13x2 Combine like terms: -42x + 42x = 0 42x + -13x2 + x3 = 0 + 13x2 + -13x2 42x + -13x2 + x3 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 42x + -13x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(42 + -13x + x2) = 0 Factor a trinomial. x((6 + -1x)(7 + -1x)) = 0Subproblem 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, 6, 7}
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