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Simplifying x((1 + -1x)(4 + -1x)) = 0 Multiply (1 + -1x) * (4 + -1x) x((1(4 + -1x) + -1x * (4 + -1x))) = 0 x(((4 * 1 + -1x * 1) + -1x * (4 + -1x))) = 0 x(((4 + -1x) + -1x * (4 + -1x))) = 0 x((4 + -1x + (4 * -1x + -1x * -1x))) = 0 x((4 + -1x + (-4x + 1x2))) = 0 Combine like terms: -1x + -4x = -5x x((4 + -5x + 1x2)) = 0 (4 * x + -5x * x + 1x2 * x) = 0 (4x + -5x2 + 1x3) = 0 Solving 4x + -5x2 + 1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -5x + x2) = 0 Factor a trinomial. x((1 + -1x)(4 + -1x)) = 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 + -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 = 1Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, 1, 4}
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