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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 = 20x (12 + 20x + 3x2) = 0 Solving 12 + 20x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(2 + 3x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 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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