(4v^2+9v-10)+(15v^2-7v+10)+(v-2)=

Solution for (4v^2+9v-10)+(15v^2-7v+10)+(v-2)= equation:

Simplifying
(4v2 + 9v + -10) + (15v2 + -7v + 10) + (v + -2) = 0

Reorder the terms:
(-10 + 9v + 4v2) + (15v2 + -7v + 10) + (v + -2) = 0

Remove parenthesis around (-10 + 9v + 4v2)
-10 + 9v + 4v2 + (15v2 + -7v + 10) + (v + -2) = 0

Reorder the terms:
-10 + 9v + 4v2 + (10 + -7v + 15v2) + (v + -2) = 0

Remove parenthesis around (10 + -7v + 15v2)
-10 + 9v + 4v2 + 10 + -7v + 15v2 + (v + -2) = 0

Reorder the terms:
-10 + 9v + 4v2 + 10 + -7v + 15v2 + (-2 + v) = 0

Remove parenthesis around (-2 + v)
-10 + 9v + 4v2 + 10 + -7v + 15v2 + -2 + v = 0

Reorder the terms:
-10 + 10 + -2 + 9v + -7v + v + 4v2 + 15v2 = 0

Combine like terms: -10 + 10 = 0
0 + -2 + 9v + -7v + v + 4v2 + 15v2 = 0
-2 + 9v + -7v + v + 4v2 + 15v2 = 0

Combine like terms: 9v + -7v = 2v
-2 + 2v + v + 4v2 + 15v2 = 0

Combine like terms: 2v + v = 3v
-2 + 3v + 4v2 + 15v2 = 0

Combine like terms: 4v2 + 15v2 = 19v2
-2 + 3v + 19v2 = 0

Solving
-2 + 3v + 19v2 = 0

Solving for variable 'v'.

Begin completing the square.  Divide all terms by
19 the coefficient of the squared term: 

Divide each side by '19'.
-0.1052631579 + 0.1578947368v + v2 = 0

Move the constant term to the right:

Add '0.1052631579' to each side of the equation.
-0.1052631579 + 0.1578947368v + 0.1052631579 + v2 = 0 + 0.1052631579

Reorder the terms:
-0.1052631579 + 0.1052631579 + 0.1578947368v + v2 = 0 + 0.1052631579

Combine like terms: -0.1052631579 + 0.1052631579 = 0.0000000000
0.0000000000 + 0.1578947368v + v2 = 0 + 0.1052631579
0.1578947368v + v2 = 0 + 0.1052631579

Combine like terms: 0 + 0.1052631579 = 0.1052631579
0.1578947368v + v2 = 0.1052631579

The v term is 0.1578947368v.  Take half its coefficient (0.0789473684).
Square it (0.006232686977) and add it to both sides.

Add '0.006232686977' to each side of the equation.
0.1578947368v + 0.006232686977 + v2 = 0.1052631579 + 0.006232686977

Reorder the terms:
0.006232686977 + 0.1578947368v + v2 = 0.1052631579 + 0.006232686977

Combine like terms: 0.1052631579 + 0.006232686977 = 0.111495844877
0.006232686977 + 0.1578947368v + v2 = 0.111495844877

Factor a perfect square on the left side:
(v + 0.0789473684)(v + 0.0789473684) = 0.111495844877

Calculate the square root of the right side: 0.333909935

Break this problem into two subproblems by setting 
(v + 0.0789473684) equal to 0.333909935 and -0.333909935.

Subproblem 1
v + 0.0789473684 = 0.333909935

Simplifying
v + 0.0789473684 = 0.333909935

Reorder the terms:
0.0789473684 + v = 0.333909935

Solving
0.0789473684 + v = 0.333909935

Solving for variable 'v'.

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

Add '-0.0789473684' to each side of the equation.
0.0789473684 + -0.0789473684 + v = 0.333909935 + -0.0789473684

Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000
0.0000000000 + v = 0.333909935 + -0.0789473684
v = 0.333909935 + -0.0789473684

Combine like terms: 0.333909935 + -0.0789473684 = 0.2549625666
v = 0.2549625666

Simplifying
v = 0.2549625666

Subproblem 2
v + 0.0789473684 = -0.333909935

Simplifying
v + 0.0789473684 = -0.333909935

Reorder the terms:
0.0789473684 + v = -0.333909935

Solving
0.0789473684 + v = -0.333909935

Solving for variable 'v'.

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

Add '-0.0789473684' to each side of the equation.
0.0789473684 + -0.0789473684 + v = -0.333909935 + -0.0789473684

Combine like terms: 0.0789473684 + -0.0789473684 = 0.0000000000
0.0000000000 + v = -0.333909935 + -0.0789473684
v = -0.333909935 + -0.0789473684

Combine like terms: -0.333909935 + -0.0789473684 = -0.4128573034
v = -0.4128573034

Simplifying
v = -0.4128573034

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.2549625666, -0.4128573034}