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Simplifying (v + -12)(v + 1) = -40 Reorder the terms: (-12 + v)(v + 1) = -40 Reorder the terms: (-12 + v)(1 + v) = -40 Multiply (-12 + v) * (1 + v) (-12(1 + v) + v(1 + v)) = -40 ((1 * -12 + v * -12) + v(1 + v)) = -40 ((-12 + -12v) + v(1 + v)) = -40 (-12 + -12v + (1 * v + v * v)) = -40 (-12 + -12v + (1v + v2)) = -40 Combine like terms: -12v + 1v = -11v (-12 + -11v + v2) = -40 Solving -12 + -11v + v2 = -40 Solving for variable 'v'. Reorder the terms: -12 + 40 + -11v + v2 = -40 + 40 Combine like terms: -12 + 40 = 28 28 + -11v + v2 = -40 + 40 Combine like terms: -40 + 40 = 0 28 + -11v + v2 = 0 Factor a trinomial. (4 + -1v)(7 + -1v) = 0Subproblem 1
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 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 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {4, 7}
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