(-1q^2+6q)-(48q+30)=

Solution for (-1q^2+6q)-(48q+30)= equation:

Simplifying
(-1q2 + 6q) + -1(48q + 30) = 0

Reorder the terms:
(6q + -1q2) + -1(48q + 30) = 0

Remove parenthesis around (6q + -1q2)
6q + -1q2 + -1(48q + 30) = 0

Reorder the terms:
6q + -1q2 + -1(30 + 48q) = 0
6q + -1q2 + (30 * -1 + 48q * -1) = 0
6q + -1q2 + (-30 + -48q) = 0

Reorder the terms:
-30 + 6q + -48q + -1q2 = 0

Combine like terms: 6q + -48q = -42q
-30 + -42q + -1q2 = 0

Solving
-30 + -42q + -1q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 42q + q2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(30 + 42q + q2)' equal to zero and attempt to solve:

Simplifying
30 + 42q + q2 = 0

Solving
30 + 42q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 42q + -30 + q2 = 0 + -30

Reorder the terms:
30 + -30 + 42q + q2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 42q + q2 = 0 + -30
42q + q2 = 0 + -30

Combine like terms: 0 + -30 = -30
42q + q2 = -30

The q term is 42q.  Take half its coefficient (21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
42q + 441 + q2 = -30 + 441

Reorder the terms:
441 + 42q + q2 = -30 + 441

Combine like terms: -30 + 441 = 411
441 + 42q + q2 = 411

Factor a perfect square on the left side:
(q + 21)(q + 21) = 411

Calculate the square root of the right side: 20.273134933

Break this problem into two subproblems by setting 
(q + 21) equal to 20.273134933 and -20.273134933.

Subproblem 1
q + 21 = 20.273134933

Simplifying
q + 21 = 20.273134933

Reorder the terms:
21 + q = 20.273134933

Solving
21 + q = 20.273134933

Solving for variable 'q'.

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

Add '-21' to each side of the equation.
21 + -21 + q = 20.273134933 + -21

Combine like terms: 21 + -21 = 0
0 + q = 20.273134933 + -21
q = 20.273134933 + -21

Combine like terms: 20.273134933 + -21 = -0.726865067
q = -0.726865067

Simplifying
q = -0.726865067

Subproblem 2
q + 21 = -20.273134933

Simplifying
q + 21 = -20.273134933

Reorder the terms:
21 + q = -20.273134933

Solving
21 + q = -20.273134933

Solving for variable 'q'.

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

Add '-21' to each side of the equation.
21 + -21 + q = -20.273134933 + -21

Combine like terms: 21 + -21 = 0
0 + q = -20.273134933 + -21
q = -20.273134933 + -21

Combine like terms: -20.273134933 + -21 = -41.273134933
q = -41.273134933

Simplifying
q = -41.273134933

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.726865067, -41.273134933}
Solution
q = {-0.726865067, -41.273134933}