(10-2q)q=4+q

Solution for (10-2q)q=4+q equation:

Simplifying
(10 + -2q) * q = 4 + q

Reorder the terms for easier multiplication:
q(10 + -2q) = 4 + q
(10 * q + -2q * q) = 4 + q
(10q + -2q2) = 4 + q

Solving
10q + -2q2 = 4 + q

Solving for variable 'q'.

Reorder the terms:
-4 + 10q + -1q + -2q2 = 4 + q + -4 + -1q

Combine like terms: 10q + -1q = 9q
-4 + 9q + -2q2 = 4 + q + -4 + -1q

Reorder the terms:
-4 + 9q + -2q2 = 4 + -4 + q + -1q

Combine like terms: 4 + -4 = 0
-4 + 9q + -2q2 = 0 + q + -1q
-4 + 9q + -2q2 = q + -1q

Combine like terms: q + -1q = 0
-4 + 9q + -2q2 = 0

Factor a trinomial.
(-4 + q)(1 + -2q) = 0

Subproblem 1
Set the factor '(-4 + q)' equal to zero and attempt to solve:

Simplifying
-4 + q = 0

Solving
-4 + q = 0

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

Add '4' to each side of the equation.
-4 + 4 + q = 0 + 4

Combine like terms: -4 + 4 = 0
0 + q = 0 + 4
q = 0 + 4

Combine like terms: 0 + 4 = 4
q = 4

Simplifying
q = 4
Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve:

Simplifying
1 + -2q = 0

Solving
1 + -2q = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2q = 0 + -1
-2q = 0 + -1

Combine like terms: 0 + -1 = -1
-2q = -1

Divide each side by '-2'.
q = 0.5

Simplifying
q = 0.5
Solution
q = {4, 0.5}