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Simplifying (x + 6)(4x + 3) = -17 Reorder the terms: (6 + x)(4x + 3) = -17 Reorder the terms: (6 + x)(3 + 4x) = -17 Multiply (6 + x) * (3 + 4x) (6(3 + 4x) + x(3 + 4x)) = -17 ((3 * 6 + 4x * 6) + x(3 + 4x)) = -17 ((18 + 24x) + x(3 + 4x)) = -17 (18 + 24x + (3 * x + 4x * x)) = -17 (18 + 24x + (3x + 4x2)) = -17 Combine like terms: 24x + 3x = 27x (18 + 27x + 4x2) = -17 Solving 18 + 27x + 4x2 = -17 Solving for variable 'x'. Reorder the terms: 18 + 17 + 27x + 4x2 = -17 + 17 Combine like terms: 18 + 17 = 35 35 + 27x + 4x2 = -17 + 17 Combine like terms: -17 + 17 = 0 35 + 27x + 4x2 = 0 Factor a trinomial. (5 + x)(7 + 4x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve: Simplifying 7 + 4x = 0 Solving 7 + 4x = 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 + 4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4x = 0 + -7 4x = 0 + -7 Combine like terms: 0 + -7 = -7 4x = -7 Divide each side by '4'. x = -1.75 Simplifying x = -1.75Solution
x = {-5, -1.75}
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