2q^2+4q-1=7q^2-7q+1

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Solution for 2q^2+4q-1=7q^2-7q+1 equation: 


Simplifying
2q2 + 4q + -1 = 7q2 + -7q + 1

Reorder the terms:
-1 + 4q + 2q2 = 7q2 + -7q + 1

Reorder the terms:
-1 + 4q + 2q2 = 1 + -7q + 7q2

Solving
-1 + 4q + 2q2 = 1 + -7q + 7q2

Solving for variable 'q'.

Reorder the terms:
-1 + -1 + 4q + 7q + 2q2 + -7q2 = 1 + -7q + 7q2 + -1 + 7q + -7q2

Combine like terms: -1 + -1 = -2
-2 + 4q + 7q + 2q2 + -7q2 = 1 + -7q + 7q2 + -1 + 7q + -7q2

Combine like terms: 4q + 7q = 11q
-2 + 11q + 2q2 + -7q2 = 1 + -7q + 7q2 + -1 + 7q + -7q2

Combine like terms: 2q2 + -7q2 = -5q2
-2 + 11q + -5q2 = 1 + -7q + 7q2 + -1 + 7q + -7q2

Reorder the terms:
-2 + 11q + -5q2 = 1 + -1 + -7q + 7q + 7q2 + -7q2

Combine like terms: 1 + -1 = 0
-2 + 11q + -5q2 = 0 + -7q + 7q + 7q2 + -7q2
-2 + 11q + -5q2 = -7q + 7q + 7q2 + -7q2

Combine like terms: -7q + 7q = 0
-2 + 11q + -5q2 = 0 + 7q2 + -7q2
-2 + 11q + -5q2 = 7q2 + -7q2

Combine like terms: 7q2 + -7q2 = 0
-2 + 11q + -5q2 = 0

Factor a trinomial.
(-2 + q)(1 + -5q) = 0


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

Simplifying
-2 + q = 0

Solving
-2 + q = 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 + q = 0 + 2

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

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

Simplifying
q = 2

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

Simplifying
1 + -5q = 0

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

Combine like terms: 1 + -1 = 0
0 + -5q = 0 + -1
-5q = 0 + -1

Combine like terms: 0 + -1 = -1
-5q = -1

Divide each side by '-5'.
q = 0.2

Simplifying
q = 0.2
Solution
q = {2, 0.2}

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