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Simplifying 6x3 = 6x(x + 30) Reorder the terms: 6x3 = 6x(30 + x) 6x3 = (30 * 6x + x * 6x) 6x3 = (180x + 6x2) Solving 6x3 = 180x + 6x2 Solving for variable 'x'. Reorder the terms: -180x + -6x2 + 6x3 = 180x + 6x2 + -180x + -6x2 Reorder the terms: -180x + -6x2 + 6x3 = 180x + -180x + 6x2 + -6x2 Combine like terms: 180x + -180x = 0 -180x + -6x2 + 6x3 = 0 + 6x2 + -6x2 -180x + -6x2 + 6x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -180x + -6x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(-30 + -1x + x2) = 0 Factor a trinomial. 6x((-5 + -1x)(6 + -1x)) = 0 Ignore the factor 6.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 '(-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 = -5Subproblem 3
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 = 6Solution
x = {0, -5, 6}
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