4q^2+8q=4q+8

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Solution for 4q^2+8q=4q+8 equation: 


Simplifying
4q2 + 8q = 4q + 8

Reorder the terms:
8q + 4q2 = 4q + 8

Reorder the terms:
8q + 4q2 = 8 + 4q

Solving
8q + 4q2 = 8 + 4q

Solving for variable 'q'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + q + q2) = 0

Factor a trinomial.
4((-2 + -1q)(1 + -1q)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1q = 0

Solving
-2 + -1q = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1q = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1q = 0 + 2
-1q = 0 + 2

Combine like terms: 0 + 2 = 2
-1q = 2

Divide each side by '-1'.
q = -2

Simplifying
q = -2

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 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 + -1q = 0 + -1

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

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

Divide each side by '-1'.
q = 1

Simplifying
q = 1
Solution
q = {-2, 1}

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