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Simplifying (v + 2)(v + -4) + -7 = 0 Reorder the terms: (2 + v)(v + -4) + -7 = 0 Reorder the terms: (2 + v)(-4 + v) + -7 = 0 Multiply (2 + v) * (-4 + v) (2(-4 + v) + v(-4 + v)) + -7 = 0 ((-4 * 2 + v * 2) + v(-4 + v)) + -7 = 0 ((-8 + 2v) + v(-4 + v)) + -7 = 0 (-8 + 2v + (-4 * v + v * v)) + -7 = 0 (-8 + 2v + (-4v + v2)) + -7 = 0 Combine like terms: 2v + -4v = -2v (-8 + -2v + v2) + -7 = 0 Reorder the terms: -8 + -7 + -2v + v2 = 0 Combine like terms: -8 + -7 = -15 -15 + -2v + v2 = 0 Solving -15 + -2v + v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(5 + -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 '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Solution
v = {-3, 5}
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