6q+40=20q^2

Solution for 6q+40=20q^2 equation:

Simplifying
6q + 40 = 20q2

Reorder the terms:
40 + 6q = 20q2

Solving
40 + 6q = 20q2

Solving for variable 'q'.

Combine like terms: 20q2 + -20q2 = 0
40 + 6q + -20q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 3q + -10q2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + 3q + -10q2)' equal to zero and attempt to solve:

Simplifying
20 + 3q + -10q2 = 0

Solving
20 + 3q + -10q2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-2 + -0.3q + q2 = 0.0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.3q + 2 + q2 = 0.0 + 2

Reorder the terms:
-2 + 2 + -0.3q + q2 = 0.0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.3q + q2 = 0.0 + 2
-0.3q + q2 = 0.0 + 2

Combine like terms: 0.0 + 2 = 2
-0.3q + q2 = 2

The q term is -0.3q.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3q + 0.0225 + q2 = 2 + 0.0225

Reorder the terms:
0.0225 + -0.3q + q2 = 2 + 0.0225

Combine like terms: 2 + 0.0225 = 2.0225
0.0225 + -0.3q + q2 = 2.0225

Factor a perfect square on the left side:
(q + -0.15)(q + -0.15) = 2.0225

Calculate the square root of the right side: 1.422146265

Break this problem into two subproblems by setting 
(q + -0.15) equal to 1.422146265 and -1.422146265.

Subproblem 1
q + -0.15 = 1.422146265

Simplifying
q + -0.15 = 1.422146265

Reorder the terms:
-0.15 + q = 1.422146265

Solving
-0.15 + q = 1.422146265

Solving for variable 'q'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + q = 1.422146265 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + q = 1.422146265 + 0.15
q = 1.422146265 + 0.15

Combine like terms: 1.422146265 + 0.15 = 1.572146265
q = 1.572146265

Simplifying
q = 1.572146265

Subproblem 2
q + -0.15 = -1.422146265

Simplifying
q + -0.15 = -1.422146265

Reorder the terms:
-0.15 + q = -1.422146265

Solving
-0.15 + q = -1.422146265

Solving for variable 'q'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + q = -1.422146265 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + q = -1.422146265 + 0.15
q = -1.422146265 + 0.15

Combine like terms: -1.422146265 + 0.15 = -1.272146265
q = -1.272146265

Simplifying
q = -1.272146265

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {1.572146265, -1.272146265}
Solution
q = {1.572146265, -1.272146265}