4v^2=6+10v

Solution for 4v^2=6+10v equation:

Simplifying
4v2 = 6 + 10v

Solving
4v2 = 6 + 10v

Solving for variable 'v'.

Reorder the terms:
-6 + -10v + 4v2 = 6 + 10v + -6 + -10v

Reorder the terms:
-6 + -10v + 4v2 = 6 + -6 + 10v + -10v

Combine like terms: 6 + -6 = 0
-6 + -10v + 4v2 = 0 + 10v + -10v
-6 + -10v + 4v2 = 10v + -10v

Combine like terms: 10v + -10v = 0
-6 + -10v + 4v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5v + 2v2) = 0

Factor a trinomial.
2((-1 + -2v)(3 + -1v)) = 0

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

Simplifying
-1 + -2v = 0

Solving
-1 + -2v = 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 + -2v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2v = 0 + 1
-2v = 0 + 1

Combine like terms: 0 + 1 = 1
-2v = 1

Divide each side by '-2'.
v = -0.5

Simplifying
v = -0.5
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 = {-0.5, 3}