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Simplifying (3x + -2)(x + 6) = 0 Reorder the terms: (-2 + 3x)(x + 6) = 0 Reorder the terms: (-2 + 3x)(6 + x) = 0 Multiply (-2 + 3x) * (6 + x) (-2(6 + x) + 3x * (6 + x)) = 0 ((6 * -2 + x * -2) + 3x * (6 + x)) = 0 ((-12 + -2x) + 3x * (6 + x)) = 0 (-12 + -2x + (6 * 3x + x * 3x)) = 0 (-12 + -2x + (18x + 3x2)) = 0 Combine like terms: -2x + 18x = 16x (-12 + 16x + 3x2) = 0 Solving -12 + 16x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-6 + -1x)(2 + -3x) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-6, 0.6666666667}
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