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Simplifying x3 + -2x2(4x + -1) + x(1 + -4x)(1 + -4x) = 0 Reorder the terms: x3 + -2x2(-1 + 4x) + x(1 + -4x)(1 + -4x) = 0 x3 + (-1 * -2x2 + 4x * -2x2) + x(1 + -4x)(1 + -4x) = 0 x3 + (2x2 + -8x3) + x(1 + -4x)(1 + -4x) = 0 Multiply (1 + -4x) * (1 + -4x) x3 + 2x2 + -8x3 + x(1(1 + -4x) + -4x * (1 + -4x)) = 0 x3 + 2x2 + -8x3 + x((1 * 1 + -4x * 1) + -4x * (1 + -4x)) = 0 x3 + 2x2 + -8x3 + x((1 + -4x) + -4x * (1 + -4x)) = 0 x3 + 2x2 + -8x3 + x(1 + -4x + (1 * -4x + -4x * -4x)) = 0 x3 + 2x2 + -8x3 + x(1 + -4x + (-4x + 16x2)) = 0 Combine like terms: -4x + -4x = -8x x3 + 2x2 + -8x3 + x(1 + -8x + 16x2) = 0 x3 + 2x2 + -8x3 + (1 * x + -8x * x + 16x2 * x) = 0 x3 + 2x2 + -8x3 + (1x + -8x2 + 16x3) = 0 Reorder the terms: 1x + 2x2 + -8x2 + x3 + -8x3 + 16x3 = 0 Combine like terms: 2x2 + -8x2 = -6x2 1x + -6x2 + x3 + -8x3 + 16x3 = 0 Combine like terms: x3 + -8x3 = -7x3 1x + -6x2 + -7x3 + 16x3 = 0 Combine like terms: -7x3 + 16x3 = 9x3 1x + -6x2 + 9x3 = 0 Solving 1x + -6x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -6x + 9x2) = 0 Factor a trinomial. x((1 + -3x)(1 + -3x)) = 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 '(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 = 0.3333333333Solution
x = {0, 0.3333333333, 0.3333333333}
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