(v-5)(v+7)=0

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Solution for (v-5)(v+7)=0 equation: 


Simplifying
(v + -5)(v + 7) = 0

Reorder the terms:
(-5 + v)(v + 7) = 0

Reorder the terms:
(-5 + v)(7 + v) = 0

Multiply (-5 + v) * (7 + v)
(-5(7 + v) + v(7 + v)) = 0
((7 * -5 + v * -5) + v(7 + v)) = 0
((-35 + -5v) + v(7 + v)) = 0
(-35 + -5v + (7 * v + v * v)) = 0
(-35 + -5v + (7v + v2)) = 0

Combine like terms: -5v + 7v = 2v
(-35 + 2v + v2) = 0

Solving
-35 + 2v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + -1v)(5 + -1v) = 0


Subproblem 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 = -7

Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-7, 5}

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