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Simplifying x3 = -19x2 + 42x Reorder the terms: x3 = 42x + -19x2 Solving x3 = 42x + -19x2 Solving for variable 'x'. Reorder the terms: -42x + 19x2 + x3 = 42x + -19x2 + -42x + 19x2 Reorder the terms: -42x + 19x2 + x3 = 42x + -42x + -19x2 + 19x2 Combine like terms: 42x + -42x = 0 -42x + 19x2 + x3 = 0 + -19x2 + 19x2 -42x + 19x2 + x3 = -19x2 + 19x2 Combine like terms: -19x2 + 19x2 = 0 -42x + 19x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-42 + 19x + x2) = 0 Factor a trinomial. x((-21 + -1x)(2 + -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 '(-21 + -1x)' equal to zero and attempt to solve: Simplifying -21 + -1x = 0 Solving -21 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1x = 0 + 21 -1x = 0 + 21 Combine like terms: 0 + 21 = 21 -1x = 21 Divide each side by '-1'. x = -21 Simplifying x = -21Subproblem 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, -21, 2}
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