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Simplifying 0 = 15x3 + -21x2 + 6x Reorder the terms: 0 = 6x + -21x2 + 15x3 Solving 0 = 6x + -21x2 + 15x3 Solving for variable 'x'. Remove the zero: -6x + 21x2 + -15x3 = 6x + -21x2 + 15x3 + -6x + 21x2 + -15x3 Reorder the terms: -6x + 21x2 + -15x3 = 6x + -6x + -21x2 + 21x2 + 15x3 + -15x3 Combine like terms: 6x + -6x = 0 -6x + 21x2 + -15x3 = 0 + -21x2 + 21x2 + 15x3 + -15x3 -6x + 21x2 + -15x3 = -21x2 + 21x2 + 15x3 + -15x3 Combine like terms: -21x2 + 21x2 = 0 -6x + 21x2 + -15x3 = 0 + 15x3 + -15x3 -6x + 21x2 + -15x3 = 15x3 + -15x3 Combine like terms: 15x3 + -15x3 = 0 -6x + 21x2 + -15x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-2 + 7x + -5x2) = 0 Factor a trinomial. 3x((-1 + x)(2 + -5x)) = 0 Ignore the factor 3.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 3
Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {0, 1, 0.4}
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