=3+q(8-4q)-8q

Solution for =3+q(8-4q)-8q equation:

Simplifying
0 = 3 + q(8 + -4q) + -8q
0 = 3 + (8 * q + -4q * q) + -8q
0 = 3 + (8q + -4q2) + -8q

Reorder the terms:
0 = 3 + 8q + -8q + -4q2

Combine like terms: 8q + -8q = 0
0 = 3 + 0 + -4q2
0 = 3 + -4q2

Solving
0 = 3 + -4q2

Solving for variable 'q'.

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

Add '4q2' to each side of the equation.
0 + 4q2 = 3 + -4q2 + 4q2
Remove the zero:
4q2 = 3 + -4q2 + 4q2

Combine like terms: -4q2 + 4q2 = 0
4q2 = 3 + 0
4q2 = 3

Divide each side by '4'.
q2 = 0.75

Simplifying
q2 = 0.75

Take the square root of each side:
q = {-0.866025404, 0.866025404}