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Simplifying (6x + 7)(x + 1) = 5 Reorder the terms: (7 + 6x)(x + 1) = 5 Reorder the terms: (7 + 6x)(1 + x) = 5 Multiply (7 + 6x) * (1 + x) (7(1 + x) + 6x * (1 + x)) = 5 ((1 * 7 + x * 7) + 6x * (1 + x)) = 5 ((7 + 7x) + 6x * (1 + x)) = 5 (7 + 7x + (1 * 6x + x * 6x)) = 5 (7 + 7x + (6x + 6x2)) = 5 Combine like terms: 7x + 6x = 13x (7 + 13x + 6x2) = 5 Solving 7 + 13x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: 7 + -5 + 13x + 6x2 = 5 + -5 Combine like terms: 7 + -5 = 2 2 + 13x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 2 + 13x + 6x2 = 0 Factor a trinomial. (2 + x)(1 + 6x) = 0Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-2, -0.1666666667}
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