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Simplifying (7 + v)(4v + 5) = 0 Reorder the terms: (7 + v)(5 + 4v) = 0 Multiply (7 + v) * (5 + 4v) (7(5 + 4v) + v(5 + 4v)) = 0 ((5 * 7 + 4v * 7) + v(5 + 4v)) = 0 ((35 + 28v) + v(5 + 4v)) = 0 (35 + 28v + (5 * v + 4v * v)) = 0 (35 + 28v + (5v + 4v2)) = 0 Combine like terms: 28v + 5v = 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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