(300-20q)q-20q-2400=0

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Solution for (300-20q)q-20q-2400=0 equation: 


Simplifying
(300 + -20q) * q + -20q + -2400 = 0

Reorder the terms for easier multiplication:
q(300 + -20q) + -20q + -2400 = 0
(300 * q + -20q * q) + -20q + -2400 = 0
(300q + -20q2) + -20q + -2400 = 0

Reorder the terms:
-2400 + 300q + -20q + -20q2 = 0

Combine like terms: 300q + -20q = 280q
-2400 + 280q + -20q2 = 0

Solving
-2400 + 280q + -20q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-120 + 14q + -1q2) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(-120 + 14q + -1q2)' equal to zero and attempt to solve:

Simplifying
-120 + 14q + -1q2 = 0

Solving
-120 + 14q + -1q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
120 + -14q + q2 = 0

Move the constant term to the right:

Add '-120' to each side of the equation.
120 + -14q + -120 + q2 = 0 + -120

Reorder the terms:
120 + -120 + -14q + q2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + -14q + q2 = 0 + -120
-14q + q2 = 0 + -120

Combine like terms: 0 + -120 = -120
-14q + q2 = -120

The q term is -14q.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14q + 49 + q2 = -120 + 49

Reorder the terms:
49 + -14q + q2 = -120 + 49

Combine like terms: -120 + 49 = -71
49 + -14q + q2 = -71

Factor a perfect square on the left side:
(q + -7)(q + -7) = -71

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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