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Simplifying (10v + 7)(3v + -7) = 0 Reorder the terms: (7 + 10v)(3v + -7) = 0 Reorder the terms: (7 + 10v)(-7 + 3v) = 0 Multiply (7 + 10v) * (-7 + 3v) (7(-7 + 3v) + 10v * (-7 + 3v)) = 0 ((-7 * 7 + 3v * 7) + 10v * (-7 + 3v)) = 0 ((-49 + 21v) + 10v * (-7 + 3v)) = 0 (-49 + 21v + (-7 * 10v + 3v * 10v)) = 0 (-49 + 21v + (-70v + 30v2)) = 0 Combine like terms: 21v + -70v = -49v (-49 + -49v + 30v2) = 0 Solving -49 + -49v + 30v2 = 0 Solving for variable 'v'. Factor a trinomial. (-7 + -10v)(7 + -3v) = 0Subproblem 1
Set the factor '(-7 + -10v)' equal to zero and attempt to solve: Simplifying -7 + -10v = 0 Solving -7 + -10v = 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 + -10v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -10v = 0 + 7 -10v = 0 + 7 Combine like terms: 0 + 7 = 7 -10v = 7 Divide each side by '-10'. v = -0.7 Simplifying v = -0.7Subproblem 2
Set the factor '(7 + -3v)' equal to zero and attempt to solve: Simplifying 7 + -3v = 0 Solving 7 + -3v = 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 + -3v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3v = 0 + -7 -3v = 0 + -7 Combine like terms: 0 + -7 = -7 -3v = -7 Divide each side by '-3'. v = 2.333333333 Simplifying v = 2.333333333Solution
v = {-0.7, 2.333333333}
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