v^2+v-53=3

Solution for v^2+v-53=3 equation:

Simplifying
v2 + v + -53 = 3

Reorder the terms:
-53 + v + v2 = 3

Solving
-53 + v + v2 = 3

Solving for variable 'v'.

Reorder the terms:
-53 + -3 + v + v2 = 3 + -3

Combine like terms: -53 + -3 = -56
-56 + v + v2 = 3 + -3

Combine like terms: 3 + -3 = 0
-56 + v + v2 = 0

Factor a trinomial.
(-8 + -1v)(7 + -1v) = 0

Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve:

Simplifying
-8 + -1v = 0

Solving
-8 + -1v = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1v = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1v = 0 + 8
-1v = 0 + 8

Combine like terms: 0 + 8 = 8
-1v = 8

Divide each side by '-1'.
v = -8

Simplifying
v = -8
Subproblem 2
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {-8, 7}