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Simplifying (x + 4)(3x + 2) = -7 Reorder the terms: (4 + x)(3x + 2) = -7 Reorder the terms: (4 + x)(2 + 3x) = -7 Multiply (4 + x) * (2 + 3x) (4(2 + 3x) + x(2 + 3x)) = -7 ((2 * 4 + 3x * 4) + x(2 + 3x)) = -7 ((8 + 12x) + x(2 + 3x)) = -7 (8 + 12x + (2 * x + 3x * x)) = -7 (8 + 12x + (2x + 3x2)) = -7 Combine like terms: 12x + 2x = 14x (8 + 14x + 3x2) = -7 Solving 8 + 14x + 3x2 = -7 Solving for variable 'x'. Reorder the terms: 8 + 7 + 14x + 3x2 = -7 + 7 Combine like terms: 8 + 7 = 15 15 + 14x + 3x2 = -7 + 7 Combine like terms: -7 + 7 = 0 15 + 14x + 3x2 = 0 Factor a trinomial. (3 + x)(5 + 3x) = 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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {-3, -1.666666667}
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