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Simplifying (x + 4)(4x + 3) = -9 Reorder the terms: (4 + x)(4x + 3) = -9 Reorder the terms: (4 + x)(3 + 4x) = -9 Multiply (4 + x) * (3 + 4x) (4(3 + 4x) + x(3 + 4x)) = -9 ((3 * 4 + 4x * 4) + x(3 + 4x)) = -9 ((12 + 16x) + x(3 + 4x)) = -9 (12 + 16x + (3 * x + 4x * x)) = -9 (12 + 16x + (3x + 4x2)) = -9 Combine like terms: 16x + 3x = 19x (12 + 19x + 4x2) = -9 Solving 12 + 19x + 4x2 = -9 Solving for variable 'x'. Reorder the terms: 12 + 9 + 19x + 4x2 = -9 + 9 Combine like terms: 12 + 9 = 21 21 + 19x + 4x2 = -9 + 9 Combine like terms: -9 + 9 = 0 21 + 19x + 4x2 = 0 Factor a trinomial. (3 + x)(7 + 4x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 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 = {-3, -1.75}
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