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Simplifying (4v + 9)(7 + v) = 0 Reorder the terms: (9 + 4v)(7 + v) = 0 Multiply (9 + 4v) * (7 + v) (9(7 + v) + 4v * (7 + v)) = 0 ((7 * 9 + v * 9) + 4v * (7 + v)) = 0 ((63 + 9v) + 4v * (7 + v)) = 0 (63 + 9v + (7 * 4v + v * 4v)) = 0 (63 + 9v + (28v + 4v2)) = 0 Combine like terms: 9v + 28v = 37v (63 + 37v + 4v2) = 0 Solving 63 + 37v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(9 + 4v) = 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 '(9 + 4v)' equal to zero and attempt to solve: Simplifying 9 + 4v = 0 Solving 9 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4v = 0 + -9 4v = 0 + -9 Combine like terms: 0 + -9 = -9 4v = -9 Divide each side by '4'. v = -2.25 Simplifying v = -2.25Solution
v = {-7, -2.25}
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