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Simplifying (5v + 7)(6 + v) = 0 Reorder the terms: (7 + 5v)(6 + v) = 0 Multiply (7 + 5v) * (6 + v) (7(6 + v) + 5v * (6 + v)) = 0 ((6 * 7 + v * 7) + 5v * (6 + v)) = 0 ((42 + 7v) + 5v * (6 + v)) = 0 (42 + 7v + (6 * 5v + v * 5v)) = 0 (42 + 7v + (30v + 5v2)) = 0 Combine like terms: 7v + 30v = 37v (42 + 37v + 5v2) = 0 Solving 42 + 37v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (6 + v)(7 + 5v) = 0Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 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 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6Subproblem 2
Set the factor '(7 + 5v)' equal to zero and attempt to solve: Simplifying 7 + 5v = 0 Solving 7 + 5v = 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 + 5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5v = 0 + -7 5v = 0 + -7 Combine like terms: 0 + -7 = -7 5v = -7 Divide each side by '5'. v = -1.4 Simplifying v = -1.4Solution
v = {-6, -1.4}
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