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Simplifying (3x + 7)(6x + 3) = 0 Reorder the terms: (7 + 3x)(6x + 3) = 0 Reorder the terms: (7 + 3x)(3 + 6x) = 0 Multiply (7 + 3x) * (3 + 6x) (7(3 + 6x) + 3x * (3 + 6x)) = 0 ((3 * 7 + 6x * 7) + 3x * (3 + 6x)) = 0 ((21 + 42x) + 3x * (3 + 6x)) = 0 (21 + 42x + (3 * 3x + 6x * 3x)) = 0 (21 + 42x + (9x + 18x2)) = 0 Combine like terms: 42x + 9x = 51x (21 + 51x + 18x2) = 0 Solving 21 + 51x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 17x + 6x2) = 0 Factor a trinomial. 3((7 + 3x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-2.333333333, -0.5}
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