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Simplifying (x + 6)(6x + 7) = 0 Reorder the terms: (6 + x)(6x + 7) = 0 Reorder the terms: (6 + x)(7 + 6x) = 0 Multiply (6 + x) * (7 + 6x) (6(7 + 6x) + x(7 + 6x)) = 0 ((7 * 6 + 6x * 6) + x(7 + 6x)) = 0 ((42 + 36x) + x(7 + 6x)) = 0 (42 + 36x + (7 * x + 6x * x)) = 0 (42 + 36x + (7x + 6x2)) = 0 Combine like terms: 36x + 7x = 43x (42 + 43x + 6x2) = 0 Solving 42 + 43x + 6x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(7 + 6x) = 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 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667Solution
x = {-6, -1.166666667}
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