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Simplifying (v + 3)(v + 1) = 15 Reorder the terms: (3 + v)(v + 1) = 15 Reorder the terms: (3 + v)(1 + v) = 15 Multiply (3 + v) * (1 + v) (3(1 + v) + v(1 + v)) = 15 ((1 * 3 + v * 3) + v(1 + v)) = 15 ((3 + 3v) + v(1 + v)) = 15 (3 + 3v + (1 * v + v * v)) = 15 (3 + 3v + (1v + v2)) = 15 Combine like terms: 3v + 1v = 4v (3 + 4v + v2) = 15 Solving 3 + 4v + v2 = 15 Solving for variable 'v'. Reorder the terms: 3 + -15 + 4v + v2 = 15 + -15 Combine like terms: 3 + -15 = -12 -12 + 4v + v2 = 15 + -15 Combine like terms: 15 + -15 = 0 -12 + 4v + v2 = 0 Factor a trinomial. (-6 + -1v)(2 + -1v) = 0Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve: Simplifying -6 + -1v = 0 Solving -6 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1v = 0 + 6 -1v = 0 + 6 Combine like terms: 0 + 6 = 6 -1v = 6 Divide each side by '-1'. v = -6 Simplifying v = -6Subproblem 2
Set the factor '(2 + -1v)' equal to zero and attempt to solve: Simplifying 2 + -1v = 0 Solving 2 + -1v = 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 + -1v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1v = 0 + -2 -1v = 0 + -2 Combine like terms: 0 + -2 = -2 -1v = -2 Divide each side by '-1'. v = 2 Simplifying v = 2Solution
v = {-6, 2}
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