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Simplifying (4v + -7)(1 + v) = 0 Reorder the terms: (-7 + 4v)(1 + v) = 0 Multiply (-7 + 4v) * (1 + v) (-7(1 + v) + 4v * (1 + v)) = 0 ((1 * -7 + v * -7) + 4v * (1 + v)) = 0 ((-7 + -7v) + 4v * (1 + v)) = 0 (-7 + -7v + (1 * 4v + v * 4v)) = 0 (-7 + -7v + (4v + 4v2)) = 0 Combine like terms: -7v + 4v = -3v (-7 + -3v + 4v2) = 0 Solving -7 + -3v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-1 + -1v)(7 + -4v) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(7 + -4v)' equal to zero and attempt to solve: Simplifying 7 + -4v = 0 Solving 7 + -4v = 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 + -4v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4v = 0 + -7 -4v = 0 + -7 Combine like terms: 0 + -7 = -7 -4v = -7 Divide each side by '-4'. v = 1.75 Simplifying v = 1.75Solution
v = {-1, 1.75}
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