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Simplifying -1(-4x + -1)(5 + -1x) * x = 0 Reorder the terms: -1(-1 + -4x)(5 + -1x) * x = 0 Reorder the terms for easier multiplication: -1x(-1 + -4x)(5 + -1x) = 0 Multiply (-1 + -4x) * (5 + -1x) -1x(-1(5 + -1x) + -4x * (5 + -1x)) = 0 -1x((5 * -1 + -1x * -1) + -4x * (5 + -1x)) = 0 -1x((-5 + 1x) + -4x * (5 + -1x)) = 0 -1x(-5 + 1x + (5 * -4x + -1x * -4x)) = 0 -1x(-5 + 1x + (-20x + 4x2)) = 0 Combine like terms: 1x + -20x = -19x -1x(-5 + -19x + 4x2) = 0 (-5 * -1x + -19x * -1x + 4x2 * -1x) = 0 (5x + 19x2 + -4x3) = 0 Solving 5x + 19x2 + -4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 19x + -4x2) = 0 Factor a trinomial. x((5 + -1x)(1 + 4x)) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 3
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {0, 5, -0.25}
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