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Simplifying (4v + 7)(2 + v) = 0 Reorder the terms: (7 + 4v)(2 + v) = 0 Multiply (7 + 4v) * (2 + v) (7(2 + v) + 4v * (2 + v)) = 0 ((2 * 7 + v * 7) + 4v * (2 + v)) = 0 ((14 + 7v) + 4v * (2 + v)) = 0 (14 + 7v + (2 * 4v + v * 4v)) = 0 (14 + 7v + (8v + 4v2)) = 0 Combine like terms: 7v + 8v = 15v (14 + 15v + 4v2) = 0 Solving 14 + 15v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + v)(7 + 4v) = 0Subproblem 1
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Subproblem 2
Set the factor '(7 + 4v)' equal to zero and attempt to solve: Simplifying 7 + 4v = 0 Solving 7 + 4v = 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 + 4v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4v = 0 + -7 4v = 0 + -7 Combine like terms: 0 + -7 = -7 4v = -7 Divide each side by '4'. v = -1.75 Simplifying v = -1.75Solution
v = {-2, -1.75}
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