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Simplifying (x + 3)(x + 4) = 6 Reorder the terms: (3 + x)(x + 4) = 6 Reorder the terms: (3 + x)(4 + x) = 6 Multiply (3 + x) * (4 + x) (3(4 + x) + x(4 + x)) = 6 ((4 * 3 + x * 3) + x(4 + x)) = 6 ((12 + 3x) + x(4 + x)) = 6 (12 + 3x + (4 * x + x * x)) = 6 (12 + 3x + (4x + x2)) = 6 Combine like terms: 3x + 4x = 7x (12 + 7x + x2) = 6 Solving 12 + 7x + x2 = 6 Solving for variable 'x'. Reorder the terms: 12 + -6 + 7x + x2 = 6 + -6 Combine like terms: 12 + -6 = 6 6 + 7x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 6 + 7x + x2 = 0 Factor a trinomial. (6 + x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-6, -1}
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