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

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

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

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

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

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

Solving for variable 'q'.

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

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

Combine like terms: 4q + -7q = -3q
-2 + -3q + 2q2 = 1 + 7q + -1 + -7q

Reorder the terms:
-2 + -3q + 2q2 = 1 + -1 + 7q + -7q

Combine like terms: 1 + -1 = 0
-2 + -3q + 2q2 = 0 + 7q + -7q
-2 + -3q + 2q2 = 7q + -7q

Combine like terms: 7q + -7q = 0
-2 + -3q + 2q2 = 0

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

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

Simplifying
-1 + -2q = 0

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

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

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

Divide each side by '-2'.
q = -0.5

Simplifying
q = -0.5
Subproblem 2
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
Solution
q = {-0.5, 2}