-4v^2-7v=-57

Solution for -4v^2-7v=-57 equation:

Simplifying
-4v2 + -7v = -57

Reorder the terms:
-7v + -4v2 = -57

Solving
-7v + -4v2 = -57

Solving for variable 'v'.

Reorder the terms:
57 + -7v + -4v2 = -57 + 57

Combine like terms: -57 + 57 = 0
57 + -7v + -4v2 = 0

Factor a trinomial.
(3 + -1v)(19 + 4v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + 4v)' equal to zero and attempt to solve:

Simplifying
19 + 4v = 0

Solving
19 + 4v = 0

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

Add '-19' to each side of the equation.
19 + -19 + 4v = 0 + -19

Combine like terms: 19 + -19 = 0
0 + 4v = 0 + -19
4v = 0 + -19

Combine like terms: 0 + -19 = -19
4v = -19

Divide each side by '4'.
v = -4.75

Simplifying
v = -4.75
Solution
v = {3, -4.75}