2v^2+9v-14=(v-4)

Solution for 2v^2+9v-14=(v-4) equation:

Simplifying
2v2 + 9v + -14 = (v + -4)

Reorder the terms:
-14 + 9v + 2v2 = (v + -4)

Reorder the terms:
-14 + 9v + 2v2 = (-4 + v)

Remove parenthesis around (-4 + v)
-14 + 9v + 2v2 = -4 + v

Solving
-14 + 9v + 2v2 = -4 + v

Solving for variable 'v'.

Reorder the terms:
-14 + 4 + 9v + -1v + 2v2 = -4 + v + 4 + -1v

Combine like terms: -14 + 4 = -10
-10 + 9v + -1v + 2v2 = -4 + v + 4 + -1v

Combine like terms: 9v + -1v = 8v
-10 + 8v + 2v2 = -4 + v + 4 + -1v

Reorder the terms:
-10 + 8v + 2v2 = -4 + 4 + v + -1v

Combine like terms: -4 + 4 = 0
-10 + 8v + 2v2 = 0 + v + -1v
-10 + 8v + 2v2 = v + -1v

Combine like terms: v + -1v = 0
-10 + 8v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4v + v2) = 0

Factor a trinomial.
2((-5 + -1v)(1 + -1v)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1v)' equal to zero and attempt to solve:

Simplifying
-5 + -1v = 0

Solving
-5 + -1v = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v = 0 + 5
-1v = 0 + 5

Combine like terms: 0 + 5 = 5
-1v = 5

Divide each side by '-1'.
v = -5

Simplifying
v = -5
Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

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

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

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

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

Simplifying
v = 1
Solution
v = {-5, 1}