4v^2=7v+2

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

Simplifying
4v2 = 7v + 2

Reorder the terms:
4v2 = 2 + 7v

Solving
4v2 = 2 + 7v

Solving for variable 'v'.

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

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

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

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

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

Subproblem 1
Set the factor '(-1 + -4v)' equal to zero and attempt to solve:

Simplifying
-1 + -4v = 0

Solving
-1 + -4v = 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 + -4v = 0 + 1

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

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

Divide each side by '-4'.
v = -0.25

Simplifying
v = -0.25
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 = {-0.25, 2}