10v^2+75v+125=0

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Solution for 10v^2+75v+125=0 equation: 


Simplifying
10v2 + 75v + 125 = 0

Reorder the terms:
125 + 75v + 10v2 = 0

Solving
125 + 75v + 10v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5'.
5(25 + 15v + 2v2) = 0

Factor a trinomial.
5((5 + v)(5 + 2v)) = 0

Ignore the factor 5.

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

Simplifying
5 + v = 0

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

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

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

Simplifying
v = -5

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

Simplifying
5 + 2v = 0

Solving
5 + 2v = 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 + 2v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2v = 0 + -5
2v = 0 + -5

Combine like terms: 0 + -5 = -5
2v = -5

Divide each side by '2'.
v = -2.5

Simplifying
v = -2.5
Solution
v = {-5, -2.5}

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