2v^2-7v=4

Solution for 2v^2-7v=4 equation:

Simplifying
2v2 + -7v = 4

Reorder the terms:
-7v + 2v2 = 4

Solving
-7v + 2v2 = 4

Solving for variable 'v'.

Reorder the terms:
-4 + -7v + 2v2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -7v + 2v2 = 0

Factor a trinomial.
(-1 + -2v)(4 + -1v) = 0

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 '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-0.5, 4}