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Simplifying (5v + -6)(7 + v) = 0 Reorder the terms: (-6 + 5v)(7 + v) = 0 Multiply (-6 + 5v) * (7 + v) (-6(7 + v) + 5v * (7 + v)) = 0 ((7 * -6 + v * -6) + 5v * (7 + v)) = 0 ((-42 + -6v) + 5v * (7 + v)) = 0 (-42 + -6v + (7 * 5v + v * 5v)) = 0 (-42 + -6v + (35v + 5v2)) = 0 Combine like terms: -6v + 35v = 29v (-42 + 29v + 5v2) = 0 Solving -42 + 29v + 5v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -1v)(6 + -5v) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(6 + -5v)' equal to zero and attempt to solve: Simplifying 6 + -5v = 0 Solving 6 + -5v = 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 + -5v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5v = 0 + -6 -5v = 0 + -6 Combine like terms: 0 + -6 = -6 -5v = -6 Divide each side by '-5'. v = 1.2 Simplifying v = 1.2Solution
v = {-7, 1.2}
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