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Simplifying (7 + v)(4v + 3) = 0 Reorder the terms: (7 + v)(3 + 4v) = 0 Multiply (7 + v) * (3 + 4v) (7(3 + 4v) + v(3 + 4v)) = 0 ((3 * 7 + 4v * 7) + v(3 + 4v)) = 0 ((21 + 28v) + v(3 + 4v)) = 0 (21 + 28v + (3 * v + 4v * v)) = 0 (21 + 28v + (3v + 4v2)) = 0 Combine like terms: 28v + 3v = 31v (21 + 31v + 4v2) = 0 Solving 21 + 31v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (7 + v)(3 + 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 '(3 + 4v)' equal to zero and attempt to solve: Simplifying 3 + 4v = 0 Solving 3 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4v = 0 + -3 4v = 0 + -3 Combine like terms: 0 + -3 = -3 4v = -3 Divide each side by '4'. v = -0.75 Simplifying v = -0.75Solution
v = {-7, -0.75}
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