-2q(q-5)=6q+10

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Solution for -2q(q-5)=6q+10 equation: 


Simplifying
-2q(q + -5) = 6q + 10

Reorder the terms:
-2q(-5 + q) = 6q + 10
(-5 * -2q + q * -2q) = 6q + 10
(10q + -2q2) = 6q + 10

Reorder the terms:
10q + -2q2 = 10 + 6q

Solving
10q + -2q2 = 10 + 6q

Solving for variable 'q'.

Reorder the terms:
-10 + 10q + -6q + -2q2 = 10 + 6q + -10 + -6q

Combine like terms: 10q + -6q = 4q
-10 + 4q + -2q2 = 10 + 6q + -10 + -6q

Reorder the terms:
-10 + 4q + -2q2 = 10 + -10 + 6q + -6q

Combine like terms: 10 + -10 = 0
-10 + 4q + -2q2 = 0 + 6q + -6q
-10 + 4q + -2q2 = 6q + -6q

Combine like terms: 6q + -6q = 0
-10 + 4q + -2q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2q + -1q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 2q + -1q2)' equal to zero and attempt to solve:

Simplifying
-5 + 2q + -1q2 = 0

Solving
-5 + 2q + -1q2 = 0

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

Divide each side by '-1'.
5 + -2q + q2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2q + -5 + q2 = 0 + -5

Reorder the terms:
5 + -5 + -2q + q2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2q + q2 = 0 + -5
-2q + q2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2q + q2 = -5

The q term is -2q.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2q + 1 + q2 = -5 + 1

Reorder the terms:
1 + -2q + q2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + -2q + q2 = -4

Factor a perfect square on the left side:
(q + -1)(q + -1) = -4

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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