4v^2-10v=-4

Solution for 4v^2-10v=-4 equation:

Simplifying
4v2 + -10v = -4

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

Solving
-10v + 4v2 = -4

Solving for variable 'v'.

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

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

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

Factor a trinomial.
2((1 + -2v)(2 + -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 '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {0.5, 2}