6q^2-8q+50=2q^2-4q+50

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Solution for 6q^2-8q+50=2q^2-4q+50 equation: 


Simplifying
6q2 + -8q + 50 = 2q2 + -4q + 50

Reorder the terms:
50 + -8q + 6q2 = 2q2 + -4q + 50

Reorder the terms:
50 + -8q + 6q2 = 50 + -4q + 2q2

Add '-50' to each side of the equation.
50 + -8q + -50 + 6q2 = 50 + -4q + -50 + 2q2

Reorder the terms:
50 + -50 + -8q + 6q2 = 50 + -4q + -50 + 2q2

Combine like terms: 50 + -50 = 0
0 + -8q + 6q2 = 50 + -4q + -50 + 2q2
-8q + 6q2 = 50 + -4q + -50 + 2q2

Reorder the terms:
-8q + 6q2 = 50 + -50 + -4q + 2q2

Combine like terms: 50 + -50 = 0
-8q + 6q2 = 0 + -4q + 2q2
-8q + 6q2 = -4q + 2q2

Solving
-8q + 6q2 = -4q + 2q2

Solving for variable 'q'.

Reorder the terms:
-8q + 4q + 6q2 + -2q2 = -4q + 2q2 + 4q + -2q2

Combine like terms: -8q + 4q = -4q
-4q + 6q2 + -2q2 = -4q + 2q2 + 4q + -2q2

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4q'.
4q(-1 + q) = 0

Ignore the factor 4.

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 '(-1 + q)' equal to zero and attempt to solve:

Simplifying
-1 + q = 0

Solving
-1 + q = 0

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

Add '1' to each side of the equation.
-1 + 1 + q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + q = 0 + 1
q = 0 + 1

Combine like terms: 0 + 1 = 1
q = 1

Simplifying
q = 1
Solution
q = {0, 1}

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