2v^2+3v-1=4

Solution for 2v^2+3v-1=4 equation:

Simplifying
2v2 + 3v + -1 = 4

Reorder the terms:
-1 + 3v + 2v2 = 4

Solving
-1 + 3v + 2v2 = 4

Solving for variable 'v'.

Reorder the terms:
-1 + -4 + 3v + 2v2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + 3v + 2v2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + 3v + 2v2 = 0

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

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

Simplifying
-5 + -2v = 0

Solving
-5 + -2v = 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 + -2v = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2v = 0 + 5
-2v = 0 + 5

Combine like terms: 0 + 5 = 5
-2v = 5

Divide each side by '-2'.
v = -2.5

Simplifying
v = -2.5
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 = {-2.5, 1}