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Simplifying 0 = 450x3 + 180x2 + 16x Reorder the terms: 0 = 16x + 180x2 + 450x3 Solving 0 = 16x + 180x2 + 450x3 Solving for variable 'x'. Remove the zero: -16x + -180x2 + -450x3 = 16x + 180x2 + 450x3 + -16x + -180x2 + -450x3 Reorder the terms: -16x + -180x2 + -450x3 = 16x + -16x + 180x2 + -180x2 + 450x3 + -450x3 Combine like terms: 16x + -16x = 0 -16x + -180x2 + -450x3 = 0 + 180x2 + -180x2 + 450x3 + -450x3 -16x + -180x2 + -450x3 = 180x2 + -180x2 + 450x3 + -450x3 Combine like terms: 180x2 + -180x2 = 0 -16x + -180x2 + -450x3 = 0 + 450x3 + -450x3 -16x + -180x2 + -450x3 = 450x3 + -450x3 Combine like terms: 450x3 + -450x3 = 0 -16x + -180x2 + -450x3 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(8 + 90x + 225x2) = 0 Factor a trinomial. -2x((4 + 15x)(2 + 15x)) = 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 '(4 + 15x)' equal to zero and attempt to solve: Simplifying 4 + 15x = 0 Solving 4 + 15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 15x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 15x = 0 + -4 15x = 0 + -4 Combine like terms: 0 + -4 = -4 15x = -4 Divide each side by '15'. x = -0.2666666667 Simplifying x = -0.2666666667Subproblem 3
Set the factor '(2 + 15x)' equal to zero and attempt to solve: Simplifying 2 + 15x = 0 Solving 2 + 15x = 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 + 15x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 15x = 0 + -2 15x = 0 + -2 Combine like terms: 0 + -2 = -2 15x = -2 Divide each side by '15'. x = -0.1333333333 Simplifying x = -0.1333333333Solution
x = {0, -0.2666666667, -0.1333333333}
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