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Simplifying v2 + 6v + 9 + 8(v + 3) + 15 = 0 Reorder the terms: v2 + 6v + 9 + 8(3 + v) + 15 = 0 v2 + 6v + 9 + (3 * 8 + v * 8) + 15 = 0 v2 + 6v + 9 + (24 + 8v) + 15 = 0 Reorder the terms: 9 + 24 + 15 + 6v + 8v + v2 = 0 Combine like terms: 9 + 24 = 33 33 + 15 + 6v + 8v + v2 = 0 Combine like terms: 33 + 15 = 48 48 + 6v + 8v + v2 = 0 Combine like terms: 6v + 8v = 14v 48 + 14v + v2 = 0 Solving 48 + 14v + v2 = 0 Solving for variable 'v'. Factor a trinomial. (8 + v)(6 + v) = 0Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve: Simplifying 8 + v = 0 Solving 8 + v = 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 + v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + v = 0 + -8 v = 0 + -8 Combine like terms: 0 + -8 = -8 v = -8 Simplifying v = -8Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 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 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6Solution
v = {-8, -6}
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