8q-3+5q(2+q)=

Solution for 8q-3+5q(2+q)= equation:

Simplifying
8q + -3 + 5q(2 + q) = 0
8q + -3 + (2 * 5q + q * 5q) = 0
8q + -3 + (10q + 5q2) = 0

Reorder the terms:
-3 + 8q + 10q + 5q2 = 0

Combine like terms: 8q + 10q = 18q
-3 + 18q + 5q2 = 0

Solving
-3 + 18q + 5q2 = 0

Solving for variable 'q'.

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

Divide each side by '5'.
-0.6 + 3.6q + q2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 3.6q + 0.6 + q2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 3.6q + q2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 3.6q + q2 = 0 + 0.6
3.6q + q2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
3.6q + q2 = 0.6

The q term is 3.6q.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6q + 3.24 + q2 = 0.6 + 3.24

Reorder the terms:
3.24 + 3.6q + q2 = 0.6 + 3.24

Combine like terms: 0.6 + 3.24 = 3.84
3.24 + 3.6q + q2 = 3.84

Factor a perfect square on the left side:
(q + 1.8)(q + 1.8) = 3.84

Calculate the square root of the right side: 1.959591794

Break this problem into two subproblems by setting 
(q + 1.8) equal to 1.959591794 and -1.959591794.

Subproblem 1
q + 1.8 = 1.959591794

Simplifying
q + 1.8 = 1.959591794

Reorder the terms:
1.8 + q = 1.959591794

Solving
1.8 + q = 1.959591794

Solving for variable 'q'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + q = 1.959591794 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + q = 1.959591794 + -1.8
q = 1.959591794 + -1.8

Combine like terms: 1.959591794 + -1.8 = 0.159591794
q = 0.159591794

Simplifying
q = 0.159591794

Subproblem 2
q + 1.8 = -1.959591794

Simplifying
q + 1.8 = -1.959591794

Reorder the terms:
1.8 + q = -1.959591794

Solving
1.8 + q = -1.959591794

Solving for variable 'q'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + q = -1.959591794 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + q = -1.959591794 + -1.8
q = -1.959591794 + -1.8

Combine like terms: -1.959591794 + -1.8 = -3.759591794
q = -3.759591794

Simplifying
q = -3.759591794

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.159591794, -3.759591794}