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Simplifying 0 = 5x3 + -35x2 + 30x Reorder the terms: 0 = 30x + -35x2 + 5x3 Solving 0 = 30x + -35x2 + 5x3 Solving for variable 'x'. Remove the zero: -30x + 35x2 + -5x3 = 30x + -35x2 + 5x3 + -30x + 35x2 + -5x3 Reorder the terms: -30x + 35x2 + -5x3 = 30x + -30x + -35x2 + 35x2 + 5x3 + -5x3 Combine like terms: 30x + -30x = 0 -30x + 35x2 + -5x3 = 0 + -35x2 + 35x2 + 5x3 + -5x3 -30x + 35x2 + -5x3 = -35x2 + 35x2 + 5x3 + -5x3 Combine like terms: -35x2 + 35x2 = 0 -30x + 35x2 + -5x3 = 0 + 5x3 + -5x3 -30x + 35x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -30x + 35x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), '5x'. 5x(-6 + 7x + -1x2) = 0 Factor a trinomial. 5x((-6 + x)(1 + -1x)) = 0 Ignore the factor 5.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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 6, 1}
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