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Simplifying 6x3 = 17x2 + -5x Reorder the terms: 6x3 = -5x + 17x2 Solving 6x3 = -5x + 17x2 Solving for variable 'x'. Reorder the terms: 5x + -17x2 + 6x3 = -5x + 17x2 + 5x + -17x2 Reorder the terms: 5x + -17x2 + 6x3 = -5x + 5x + 17x2 + -17x2 Combine like terms: -5x + 5x = 0 5x + -17x2 + 6x3 = 0 + 17x2 + -17x2 5x + -17x2 + 6x3 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 5x + -17x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -17x + 6x2) = 0 Factor a trinomial. x((1 + -3x)(5 + -2x)) = 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 '(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 = 0.3333333333Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, 0.3333333333, 2.5}
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