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