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Simplifying v2 + -4v = 3v + 30 Reorder the terms: -4v + v2 = 3v + 30 Reorder the terms: -4v + v2 = 30 + 3v Solving -4v + v2 = 30 + 3v Solving for variable 'v'. Reorder the terms: -30 + -4v + -3v + v2 = 30 + 3v + -30 + -3v Combine like terms: -4v + -3v = -7v -30 + -7v + v2 = 30 + 3v + -30 + -3v Reorder the terms: -30 + -7v + v2 = 30 + -30 + 3v + -3v Combine like terms: 30 + -30 = 0 -30 + -7v + v2 = 0 + 3v + -3v -30 + -7v + v2 = 3v + -3v Combine like terms: 3v + -3v = 0 -30 + -7v + v2 = 0 Factor a trinomial. (-3 + -1v)(10 + -1v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 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 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 2
Set the factor '(10 + -1v)' equal to zero and attempt to solve: Simplifying 10 + -1v = 0 Solving 10 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1v = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1v = 0 + -10 -1v = 0 + -10 Combine like terms: 0 + -10 = -10 -1v = -10 Divide each side by '-1'. v = 10 Simplifying v = 10Solution
v = {-3, 10}
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