r^2+4r-54=6

Solution for r^2+4r-54=6 equation:

Simplifying
r2 + 4r + -54 = 6

Reorder the terms:
-54 + 4r + r2 = 6

Solving
-54 + 4r + r2 = 6

Solving for variable 'r'.

Reorder the terms:
-54 + -6 + 4r + r2 = 6 + -6

Combine like terms: -54 + -6 = -60
-60 + 4r + r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-60 + 4r + r2 = 0

Factor a trinomial.
(-10 + -1r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1r = 0 + -6
-1r = 0 + -6

Combine like terms: 0 + -6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6
Solution
r = {-10, 6}