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Simplifying (8x + 6)(7x + 9) = 0 Reorder the terms: (6 + 8x)(7x + 9) = 0 Reorder the terms: (6 + 8x)(9 + 7x) = 0 Multiply (6 + 8x) * (9 + 7x) (6(9 + 7x) + 8x * (9 + 7x)) = 0 ((9 * 6 + 7x * 6) + 8x * (9 + 7x)) = 0 ((54 + 42x) + 8x * (9 + 7x)) = 0 (54 + 42x + (9 * 8x + 7x * 8x)) = 0 (54 + 42x + (72x + 56x2)) = 0 Combine like terms: 42x + 72x = 114x (54 + 114x + 56x2) = 0 Solving 54 + 114x + 56x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 57x + 28x2) = 0 Factor a trinomial. 2((9 + 7x)(3 + 4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 7x)' equal to zero and attempt to solve: Simplifying 9 + 7x = 0 Solving 9 + 7x = 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 + 7x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7x = 0 + -9 7x = 0 + -9 Combine like terms: 0 + -9 = -9 7x = -9 Divide each side by '7'. x = -1.285714286 Simplifying x = -1.285714286Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-1.285714286, -0.75}
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