(9+v)(2v-7)=0

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Solution for (9+v)(2v-7)=0 equation:


Simplifying
(9 + v)(2v + -7) = 0

Reorder the terms:
(9 + v)(-7 + 2v) = 0

Multiply (9 + v) * (-7 + 2v)
(9(-7 + 2v) + v(-7 + 2v)) = 0
((-7 * 9 + 2v * 9) + v(-7 + 2v)) = 0
((-63 + 18v) + v(-7 + 2v)) = 0
(-63 + 18v + (-7 * v + 2v * v)) = 0
(-63 + 18v + (-7v + 2v2)) = 0

Combine like terms: 18v + -7v = 11v
(-63 + 11v + 2v2) = 0

Solving
-63 + 11v + 2v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-9 + -1v)(7 + -2v) = 0

Subproblem 1

Set the factor '(-9 + -1v)' equal to zero and attempt to solve: Simplifying -9 + -1v = 0 Solving -9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1v = 0 + 9 -1v = 0 + 9 Combine like terms: 0 + 9 = 9 -1v = 9 Divide each side by '-1'. v = -9 Simplifying v = -9

Subproblem 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 = 3.5

Solution

v = {-9, 3.5}

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