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Simplifying 6(x + -4) = -6x + 6(x2 + -7) Reorder the terms: 6(-4 + x) = -6x + 6(x2 + -7) (-4 * 6 + x * 6) = -6x + 6(x2 + -7) (-24 + 6x) = -6x + 6(x2 + -7) Reorder the terms: -24 + 6x = -6x + 6(-7 + x2) -24 + 6x = -6x + (-7 * 6 + x2 * 6) -24 + 6x = -6x + (-42 + 6x2) Reorder the terms: -24 + 6x = -42 + -6x + 6x2 Solving -24 + 6x = -42 + -6x + 6x2 Solving for variable 'x'. Reorder the terms: -24 + 42 + 6x + 6x + -6x2 = -42 + -6x + 6x2 + 42 + 6x + -6x2 Combine like terms: -24 + 42 = 18 18 + 6x + 6x + -6x2 = -42 + -6x + 6x2 + 42 + 6x + -6x2 Combine like terms: 6x + 6x = 12x 18 + 12x + -6x2 = -42 + -6x + 6x2 + 42 + 6x + -6x2 Reorder the terms: 18 + 12x + -6x2 = -42 + 42 + -6x + 6x + 6x2 + -6x2 Combine like terms: -42 + 42 = 0 18 + 12x + -6x2 = 0 + -6x + 6x + 6x2 + -6x2 18 + 12x + -6x2 = -6x + 6x + 6x2 + -6x2 Combine like terms: -6x + 6x = 0 18 + 12x + -6x2 = 0 + 6x2 + -6x2 18 + 12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 18 + 12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 2x + -1x2) = 0 Factor a trinomial. 6((3 + -1x)(1 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {3, -1}
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