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Simplifying (7v + -6)(4v + 7) = 0 Reorder the terms: (-6 + 7v)(4v + 7) = 0 Reorder the terms: (-6 + 7v)(7 + 4v) = 0 Multiply (-6 + 7v) * (7 + 4v) (-6(7 + 4v) + 7v * (7 + 4v)) = 0 ((7 * -6 + 4v * -6) + 7v * (7 + 4v)) = 0 ((-42 + -24v) + 7v * (7 + 4v)) = 0 (-42 + -24v + (7 * 7v + 4v * 7v)) = 0 (-42 + -24v + (49v + 28v2)) = 0 Combine like terms: -24v + 49v = 25v (-42 + 25v + 28v2) = 0 Solving -42 + 25v + 28v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -4v)(6 + -7v) = 0Subproblem 1
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 = -1.75Subproblem 2
Set the factor '(6 + -7v)' equal to zero and attempt to solve: Simplifying 6 + -7v = 0 Solving 6 + -7v = 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 + -7v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7v = 0 + -6 -7v = 0 + -6 Combine like terms: 0 + -6 = -6 -7v = -6 Divide each side by '-7'. v = 0.8571428571 Simplifying v = 0.8571428571Solution
v = {-1.75, 0.8571428571}
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