-4q^2+3q=-1

Solution for -4q^2+3q=-1 equation:

Simplifying
-4q2 + 3q = -1

Reorder the terms:
3q + -4q2 = -1

Solving
3q + -4q2 = -1

Solving for variable 'q'.

Reorder the terms:
1 + 3q + -4q2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 3q + -4q2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4q)' equal to zero and attempt to solve:

Simplifying
1 + 4q = 0

Solving
1 + 4q = 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 + 4q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4q = 0 + -1
4q = 0 + -1

Combine like terms: 0 + -1 = -1
4q = -1

Divide each side by '4'.
q = -0.25

Simplifying
q = -0.25
Solution
q = {1, -0.25}