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Simplifying (5v + 6)(7 + v) = 0 Reorder the terms: (6 + 5v)(7 + v) = 0 Multiply (6 + 5v) * (7 + v) (6(7 + v) + 5v * (7 + v)) = 0 ((7 * 6 + v * 6) + 5v * (7 + v)) = 0 ((42 + 6v) + 5v * (7 + v)) = 0 (42 + 6v + (7 * 5v + v * 5v)) = 0 (42 + 6v + (35v + 5v2)) = 0 Combine like terms: 6v + 35v = 41v (42 + 41v + 5v2) = 0 Solving 42 + 41v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(6 + 5v) = 0Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7Subproblem 2
Set the factor '(6 + 5v)' equal to zero and attempt to solve: Simplifying 6 + 5v = 0 Solving 6 + 5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + 5v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5v = 0 + -6 5v = 0 + -6 Combine like terms: 0 + -6 = -6 5v = -6 Divide each side by '5'. v = -1.2 Simplifying v = -1.2Solution
v = {-7, -1.2}
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