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Simplifying 21x3 = 13x2 + -2x Reorder the terms: 21x3 = -2x + 13x2 Solving 21x3 = -2x + 13x2 Solving for variable 'x'. Reorder the terms: 2x + -13x2 + 21x3 = -2x + 13x2 + 2x + -13x2 Reorder the terms: 2x + -13x2 + 21x3 = -2x + 2x + 13x2 + -13x2 Combine like terms: -2x + 2x = 0 2x + -13x2 + 21x3 = 0 + 13x2 + -13x2 2x + -13x2 + 21x3 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 2x + -13x2 + 21x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -13x + 21x2) = 0 Factor a trinomial. x((2 + -7x)(1 + -3x)) = 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 '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {0, 0.2857142857, 0.3333333333}
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