8v^2=25v-3

Solution for 8v^2=25v-3 equation:

Simplifying
8v2 = 25v + -3

Reorder the terms:
8v2 = -3 + 25v

Solving
8v2 = -3 + 25v

Solving for variable 'v'.

Reorder the terms:
3 + -25v + 8v2 = -3 + 25v + 3 + -25v

Reorder the terms:
3 + -25v + 8v2 = -3 + 3 + 25v + -25v

Combine like terms: -3 + 3 = 0
3 + -25v + 8v2 = 0 + 25v + -25v
3 + -25v + 8v2 = 25v + -25v

Combine like terms: 25v + -25v = 0
3 + -25v + 8v2 = 0

Factor a trinomial.
(1 + -8v)(3 + -1v) = 0

Subproblem 1
Set the factor '(1 + -8v)' equal to zero and attempt to solve:

Simplifying
1 + -8v = 0

Solving
1 + -8v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -8v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8v = 0 + -1
-8v = 0 + -1

Combine like terms: 0 + -1 = -1
-8v = -1

Divide each side by '-8'.
v = 0.125

Simplifying
v = 0.125
Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {0.125, 3}