7v^2+8v-12=0

Solution for 7v^2+8v-12=0 equation:

Simplifying
7v2 + 8v + -12 = 0

Reorder the terms:
-12 + 8v + 7v2 = 0

Solving
-12 + 8v + 7v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-2 + -1v)(6 + -7v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -7v)' equal to zero and attempt to solve:

Simplifying
6 + -7v = 0

Solving
6 + -7v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7v = 0 + -6
-7v = 0 + -6

Combine like terms: 0 + -6 = -6
-7v = -6

Divide each side by '-7'.
v = 0.8571428571

Simplifying
v = 0.8571428571
Solution
v = {-2, 0.8571428571}