12-0.4Q=5+4Q+0.6Q(Q)

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Solution for 12-0.4Q=5+4Q+0.6Q(Q) equation: 


Simplifying
12 + -0.4Q = 5 + 4Q + 0.6Q(Q)

Multiply Q * Q
12 + -0.4Q = 5 + 4Q + 0.6Q2

Solving
12 + -0.4Q = 5 + 4Q + 0.6Q2

Solving for variable 'Q'.

Reorder the terms:
12 + -5 + -0.4Q + -4Q + -0.6Q2 = 5 + 4Q + 0.6Q2 + -5 + -4Q + -0.6Q2

Combine like terms: 12 + -5 = 7
7 + -0.4Q + -4Q + -0.6Q2 = 5 + 4Q + 0.6Q2 + -5 + -4Q + -0.6Q2

Combine like terms: -0.4Q + -4Q = -4.4Q
7 + -4.4Q + -0.6Q2 = 5 + 4Q + 0.6Q2 + -5 + -4Q + -0.6Q2

Reorder the terms:
7 + -4.4Q + -0.6Q2 = 5 + -5 + 4Q + -4Q + 0.6Q2 + -0.6Q2

Combine like terms: 5 + -5 = 0
7 + -4.4Q + -0.6Q2 = 0 + 4Q + -4Q + 0.6Q2 + -0.6Q2
7 + -4.4Q + -0.6Q2 = 4Q + -4Q + 0.6Q2 + -0.6Q2

Combine like terms: 4Q + -4Q = 0
7 + -4.4Q + -0.6Q2 = 0 + 0.6Q2 + -0.6Q2
7 + -4.4Q + -0.6Q2 = 0.6Q2 + -0.6Q2

Combine like terms: 0.6Q2 + -0.6Q2 = 0.0
7 + -4.4Q + -0.6Q2 = 0.0

Begin completing the square.  Divide all terms by
-0.6 the coefficient of the squared term: 

Divide each side by '-0.6'.
-11.66666667 + 7.333333333Q + Q2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 7.333333333Q + 11.66666667 + Q2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 7.333333333Q + Q2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 7.333333333Q + Q2 = 0 + 11.66666667
7.333333333Q + Q2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
7.333333333Q + Q2 = 11.66666667

The Q term is 7.333333333Q.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333Q + 13.44444445 + Q2 = 11.66666667 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333Q + Q2 = 11.66666667 + 13.44444445

Combine like terms: 11.66666667 + 13.44444445 = 25.11111112
13.44444445 + 7.333333333Q + Q2 = 25.11111112

Factor a perfect square on the left side:
(Q + 3.666666667)(Q + 3.666666667) = 25.11111112

Calculate the square root of the right side: 5.011098794

Break this problem into two subproblems by setting 
(Q + 3.666666667) equal to 5.011098794 and -5.011098794.


Subproblem 1
Q + 3.666666667 = 5.011098794

Simplifying
Q + 3.666666667 = 5.011098794

Reorder the terms:
3.666666667 + Q = 5.011098794

Solving
3.666666667 + Q = 5.011098794

Solving for variable 'Q'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + Q = 5.011098794 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + Q = 5.011098794 + -3.666666667
Q = 5.011098794 + -3.666666667

Combine like terms: 5.011098794 + -3.666666667 = 1.344432127
Q = 1.344432127

Simplifying
Q = 1.344432127


Subproblem 2
Q + 3.666666667 = -5.011098794

Simplifying
Q + 3.666666667 = -5.011098794

Reorder the terms:
3.666666667 + Q = -5.011098794

Solving
3.666666667 + Q = -5.011098794

Solving for variable 'Q'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + Q = -5.011098794 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + Q = -5.011098794 + -3.666666667
Q = -5.011098794 + -3.666666667

Combine like terms: -5.011098794 + -3.666666667 = -8.677765461
Q = -8.677765461

Simplifying
Q = -8.677765461


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {1.344432127, -8.677765461}

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