2v^2+19v=10v+45

Solution for 2v^2+19v=10v+45 equation:

Simplifying
2v2 + 19v = 10v + 45

Reorder the terms:
19v + 2v2 = 10v + 45

Reorder the terms:
19v + 2v2 = 45 + 10v

Solving
19v + 2v2 = 45 + 10v

Solving for variable 'v'.

Reorder the terms:
-45 + 19v + -10v + 2v2 = 45 + 10v + -45 + -10v

Combine like terms: 19v + -10v = 9v
-45 + 9v + 2v2 = 45 + 10v + -45 + -10v

Reorder the terms:
-45 + 9v + 2v2 = 45 + -45 + 10v + -10v

Combine like terms: 45 + -45 = 0
-45 + 9v + 2v2 = 0 + 10v + -10v
-45 + 9v + 2v2 = 10v + -10v

Combine like terms: 10v + -10v = 0
-45 + 9v + 2v2 = 0

Factor a trinomial.
(-15 + -2v)(3 + -1v) = 0

Subproblem 1
Set the factor '(-15 + -2v)' equal to zero and attempt to solve:

Simplifying
-15 + -2v = 0

Solving
-15 + -2v = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2v = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2v = 0 + 15
-2v = 0 + 15

Combine like terms: 0 + 15 = 15
-2v = 15

Divide each side by '-2'.
v = -7.5

Simplifying
v = -7.5
Subproblem 2
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
Solution
v = {-7.5, 3}