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Simplifying x(x + -1)(x + -6) = 0 Reorder the terms: x(-1 + x)(x + -6) = 0 Reorder the terms: x(-1 + x)(-6 + x) = 0 Multiply (-1 + x) * (-6 + x) x(-1(-6 + x) + x(-6 + x)) = 0 x((-6 * -1 + x * -1) + x(-6 + x)) = 0 x((6 + -1x) + x(-6 + x)) = 0 x(6 + -1x + (-6 * x + x * x)) = 0 x(6 + -1x + (-6x + x2)) = 0 Combine like terms: -1x + -6x = -7x x(6 + -7x + x2) = 0 (6 * x + -7x * x + x2 * x) = 0 (6x + -7x2 + x3) = 0 Solving 6x + -7x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -7x + x2) = 0 Factor a trinomial. x((1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 1, 6}
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