5q(10-4q)5=-25

Solution for 5q(10-4q)5=-25 equation:

Simplifying
5q(10 + -4q) * 5 = -25

Reorder the terms for easier multiplication:
5 * 5q(10 + -4q) = -25

Multiply 5 * 5
25q(10 + -4q) = -25
(10 * 25q + -4q * 25q) = -25
(250q + -100q2) = -25

Solving
250q + -100q2 = -25

Solving for variable 'q'.

Reorder the terms:
25 + 250q + -100q2 = -25 + 25

Combine like terms: -25 + 25 = 0
25 + 250q + -100q2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(1 + 10q + -4q2) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(1 + 10q + -4q2)' equal to zero and attempt to solve:

Simplifying
1 + 10q + -4q2 = 0

Solving
1 + 10q + -4q2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -2.5q + q2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.5q + 0.25 + q2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.5q + q2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.5q + q2 = 0 + 0.25
-2.5q + q2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.5q + q2 = 0.25

The q term is -2.5q.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5q + 1.5625 + q2 = 0.25 + 1.5625

Reorder the terms:
1.5625 + -2.5q + q2 = 0.25 + 1.5625

Combine like terms: 0.25 + 1.5625 = 1.8125
1.5625 + -2.5q + q2 = 1.8125

Factor a perfect square on the left side:
(q + -1.25)(q + -1.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(q + -1.25) equal to 1.346291202 and -1.346291202.

Subproblem 1
q + -1.25 = 1.346291202

Simplifying
q + -1.25 = 1.346291202

Reorder the terms:
-1.25 + q = 1.346291202

Solving
-1.25 + q = 1.346291202

Solving for variable 'q'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + q = 1.346291202 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + q = 1.346291202 + 1.25
q = 1.346291202 + 1.25

Combine like terms: 1.346291202 + 1.25 = 2.596291202
q = 2.596291202

Simplifying
q = 2.596291202

Subproblem 2
q + -1.25 = -1.346291202

Simplifying
q + -1.25 = -1.346291202

Reorder the terms:
-1.25 + q = -1.346291202

Solving
-1.25 + q = -1.346291202

Solving for variable 'q'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + q = -1.346291202 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + q = -1.346291202 + 1.25
q = -1.346291202 + 1.25

Combine like terms: -1.346291202 + 1.25 = -0.096291202
q = -0.096291202

Simplifying
q = -0.096291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {2.596291202, -0.096291202}
Solution
q = {2.596291202, -0.096291202}