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Simplifying (3x + 84)(8x + 9) = 0 Reorder the terms: (84 + 3x)(8x + 9) = 0 Reorder the terms: (84 + 3x)(9 + 8x) = 0 Multiply (84 + 3x) * (9 + 8x) (84(9 + 8x) + 3x * (9 + 8x)) = 0 ((9 * 84 + 8x * 84) + 3x * (9 + 8x)) = 0 ((756 + 672x) + 3x * (9 + 8x)) = 0 (756 + 672x + (9 * 3x + 8x * 3x)) = 0 (756 + 672x + (27x + 24x2)) = 0 Combine like terms: 672x + 27x = 699x (756 + 699x + 24x2) = 0 Solving 756 + 699x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(252 + 233x + 8x2) = 0 Factor a trinomial. 3((28 + x)(9 + 8x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(28 + x)' equal to zero and attempt to solve: Simplifying 28 + x = 0 Solving 28 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 0 + -28 Combine like terms: 28 + -28 = 0 0 + x = 0 + -28 x = 0 + -28 Combine like terms: 0 + -28 = -28 x = -28 Simplifying x = -28Subproblem 2
Set the factor '(9 + 8x)' equal to zero and attempt to solve: Simplifying 9 + 8x = 0 Solving 9 + 8x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x = 0 + -9 8x = 0 + -9 Combine like terms: 0 + -9 = -9 8x = -9 Divide each side by '8'. x = -1.125 Simplifying x = -1.125Solution
x = {-28, -1.125}
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