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Simplifying 4(v + 6)(-1v + -7) = 0 Reorder the terms: 4(6 + v)(-1v + -7) = 0 Reorder the terms: 4(6 + v)(-7 + -1v) = 0 Multiply (6 + v) * (-7 + -1v) 4(6(-7 + -1v) + v(-7 + -1v)) = 0 4((-7 * 6 + -1v * 6) + v(-7 + -1v)) = 0 4((-42 + -6v) + v(-7 + -1v)) = 0 4(-42 + -6v + (-7 * v + -1v * v)) = 0 4(-42 + -6v + (-7v + -1v2)) = 0 Combine like terms: -6v + -7v = -13v 4(-42 + -13v + -1v2) = 0 (-42 * 4 + -13v * 4 + -1v2 * 4) = 0 (-168 + -52v + -4v2) = 0 Solving -168 + -52v + -4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '-4'. -4(42 + 13v + v2) = 0 Factor a trinomial. -4((7 + v)(6 + v)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7Subproblem 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 = {-7, -6}
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