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Simplifying (4v + 5)(v + 7) = 0 Reorder the terms: (5 + 4v)(v + 7) = 0 Reorder the terms: (5 + 4v)(7 + v) = 0 Multiply (5 + 4v) * (7 + v) (5(7 + v) + 4v * (7 + v)) = 0 ((7 * 5 + v * 5) + 4v * (7 + v)) = 0 ((35 + 5v) + 4v * (7 + v)) = 0 (35 + 5v + (7 * 4v + v * 4v)) = 0 (35 + 5v + (28v + 4v2)) = 0 Combine like terms: 5v + 28v = 33v (35 + 33v + 4v2) = 0 Solving 35 + 33v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(5 + 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 '(5 + 4v)' equal to zero and attempt to solve: Simplifying 5 + 4v = 0 Solving 5 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4v = 0 + -5 4v = 0 + -5 Combine like terms: 0 + -5 = -5 4v = -5 Divide each side by '4'. v = -1.25 Simplifying v = -1.25Solution
v = {-7, -1.25}
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