5v^2+2=-7v

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

Simplifying
5v2 + 2 = -7v

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

Solving
2 + 5v2 = -7v

Solving for variable 'v'.

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

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

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

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Subproblem 2
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
Solution
v = {-1, -0.4}