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Simplifying 32 = v(v + -4) Reorder the terms: 32 = v(-4 + v) 32 = (-4 * v + v * v) 32 = (-4v + v2) Solving 32 = -4v + v2 Solving for variable 'v'. Reorder the terms: 32 + 4v + -1v2 = -4v + 4v + v2 + -1v2 Combine like terms: -4v + 4v = 0 32 + 4v + -1v2 = 0 + v2 + -1v2 32 + 4v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 32 + 4v + -1v2 = 0 Factor a trinomial. (8 + -1v)(4 + v) = 0Subproblem 1
Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Solution
v = {8, -4}
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