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Simplifying (x + 7)(3x + 4) = -14 Reorder the terms: (7 + x)(3x + 4) = -14 Reorder the terms: (7 + x)(4 + 3x) = -14 Multiply (7 + x) * (4 + 3x) (7(4 + 3x) + x(4 + 3x)) = -14 ((4 * 7 + 3x * 7) + x(4 + 3x)) = -14 ((28 + 21x) + x(4 + 3x)) = -14 (28 + 21x + (4 * x + 3x * x)) = -14 (28 + 21x + (4x + 3x2)) = -14 Combine like terms: 21x + 4x = 25x (28 + 25x + 3x2) = -14 Solving 28 + 25x + 3x2 = -14 Solving for variable 'x'. Reorder the terms: 28 + 14 + 25x + 3x2 = -14 + 14 Combine like terms: 28 + 14 = 42 42 + 25x + 3x2 = -14 + 14 Combine like terms: -14 + 14 = 0 42 + 25x + 3x2 = 0 Factor a trinomial. (6 + x)(7 + 3x) = 0Subproblem 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 '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 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 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Solution
x = {-6, -2.333333333}
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