H(q)=3q-2(q^2-4q)

Solution for H(q)=3q-2(q^2-4q) equation:

Simplifying
H(q) = 3q + -2(q2 + -4q)

Multiply H * q
qH = 3q + -2(q2 + -4q)

Reorder the terms:
qH = 3q + -2(-4q + q2)
qH = 3q + (-4q * -2 + q2 * -2)
qH = 3q + (8q + -2q2)

Combine like terms: 3q + 8q = 11q
qH = 11q + -2q2

Solving
qH = 11q + -2q2

Solving for variable 'q'.

Reorder the terms:
-11q + qH + 2q2 = 11q + -2q2 + -11q + 2q2

Reorder the terms:
-11q + qH + 2q2 = 11q + -11q + -2q2 + 2q2

Combine like terms: 11q + -11q = 0
-11q + qH + 2q2 = 0 + -2q2 + 2q2
-11q + qH + 2q2 = -2q2 + 2q2

Combine like terms: -2q2 + 2q2 = 0
-11q + qH + 2q2 = 0

Factor out the Greatest Common Factor (GCF), 'q'.
q(-11 + H + 2q) = 0

Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0
Subproblem 2
Set the factor '(-11 + H + 2q)' equal to zero and attempt to solve:

Simplifying
-11 + H + 2q = 0

Solving
-11 + H + 2q = 0

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

Add '11' to each side of the equation.
-11 + H + 11 + 2q = 0 + 11

Reorder the terms:
-11 + 11 + H + 2q = 0 + 11

Combine like terms: -11 + 11 = 0
0 + H + 2q = 0 + 11
H + 2q = 0 + 11

Combine like terms: 0 + 11 = 11
H + 2q = 11

Add '-1H' to each side of the equation.
H + -1H + 2q = 11 + -1H

Combine like terms: H + -1H = 0
0 + 2q = 11 + -1H
2q = 11 + -1H

Divide each side by '2'.
q = 5.5 + -0.5H

Simplifying
q = 5.5 + -0.5H
Solution
q = {0, 5.5 + -0.5H}