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Simplifying (-2v + 7)(5 + -3v) = 0 Reorder the terms: (7 + -2v)(5 + -3v) = 0 Multiply (7 + -2v) * (5 + -3v) (7(5 + -3v) + -2v * (5 + -3v)) = 0 ((5 * 7 + -3v * 7) + -2v * (5 + -3v)) = 0 ((35 + -21v) + -2v * (5 + -3v)) = 0 (35 + -21v + (5 * -2v + -3v * -2v)) = 0 (35 + -21v + (-10v + 6v2)) = 0 Combine like terms: -21v + -10v = -31v (35 + -31v + 6v2) = 0 Solving 35 + -31v + 6v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + -3v)(7 + -2v) = 0Subproblem 1
Set the factor '(5 + -3v)' equal to zero and attempt to solve: Simplifying 5 + -3v = 0 Solving 5 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3v = 0 + -5 -3v = 0 + -5 Combine like terms: 0 + -5 = -5 -3v = -5 Divide each side by '-3'. v = 1.666666667 Simplifying v = 1.666666667Subproblem 2
Set the factor '(7 + -2v)' equal to zero and attempt to solve: Simplifying 7 + -2v = 0 Solving 7 + -2v = 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 + -2v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2v = 0 + -7 -2v = 0 + -7 Combine like terms: 0 + -7 = -7 -2v = -7 Divide each side by '-2'. v = 3.5 Simplifying v = 3.5Solution
v = {1.666666667, 3.5}
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