-q^2+5q-4=0

Solution for -q^2+5q-4=0 equation:

Simplifying
-1q2 + 5q + -4 = 0

Reorder the terms:
-4 + 5q + -1q2 = 0

Solving
-4 + 5q + -1q2 = 0

Solving for variable 'q'.

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

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

Simplifying
-4 + q = 0

Solving
-4 + q = 0

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

Add '4' to each side of the equation.
-4 + 4 + q = 0 + 4

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

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

Simplifying
q = 4
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 = {4, 1}