5v^2=7v-2

Solution for 5v^2=7v-2 equation:

Simplifying
5v2 = 7v + -2

Reorder the terms:
5v2 = -2 + 7v

Solving
5v2 = -2 + 7v

Solving for variable 'v'.

Reorder the terms:
2 + -7v + 5v2 = -2 + 7v + 2 + -7v

Reorder the terms:
2 + -7v + 5v2 = -2 + 2 + 7v + -7v

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

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

Factor a trinomial.
(2 + -5v)(1 + -1v) = 0

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

Simplifying
2 + -5v = 0

Solving
2 + -5v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5v = 0 + -2

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

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

Divide each side by '-5'.
v = 0.4

Simplifying
v = 0.4
Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

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

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

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

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

Simplifying
v = 1
Solution
v = {0.4, 1}