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Simplifying 6x3 = 34x2 + -20x Reorder the terms: 6x3 = -20x + 34x2 Solving 6x3 = -20x + 34x2 Solving for variable 'x'. Reorder the terms: 20x + -34x2 + 6x3 = -20x + 34x2 + 20x + -34x2 Reorder the terms: 20x + -34x2 + 6x3 = -20x + 20x + 34x2 + -34x2 Combine like terms: -20x + 20x = 0 20x + -34x2 + 6x3 = 0 + 34x2 + -34x2 20x + -34x2 + 6x3 = 34x2 + -34x2 Combine like terms: 34x2 + -34x2 = 0 20x + -34x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(10 + -17x + 3x2) = 0 Factor a trinomial. 2x((2 + -3x)(5 + -1x)) = 0 Ignore the factor 2.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 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, 0.6666666667, 5}
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