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Simplifying 17(x + 6)(4x + 3) = 0 Reorder the terms: 17(6 + x)(4x + 3) = 0 Reorder the terms: 17(6 + x)(3 + 4x) = 0 Multiply (6 + x) * (3 + 4x) 17(6(3 + 4x) + x(3 + 4x)) = 0 17((3 * 6 + 4x * 6) + x(3 + 4x)) = 0 17((18 + 24x) + x(3 + 4x)) = 0 17(18 + 24x + (3 * x + 4x * x)) = 0 17(18 + 24x + (3x + 4x2)) = 0 Combine like terms: 24x + 3x = 27x 17(18 + 27x + 4x2) = 0 (18 * 17 + 27x * 17 + 4x2 * 17) = 0 (306 + 459x + 68x2) = 0 Solving 306 + 459x + 68x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '17'. 17(18 + 27x + 4x2) = 0 Factor a trinomial. 17((6 + x)(3 + 4x)) = 0 Ignore the factor 17.Subproblem 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 '(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 = {-6, -0.75}
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