3r^2-5r-54=-4

Solution for 3r^2-5r-54=-4 equation:

Simplifying
3r2 + -5r + -54 = -4

Reorder the terms:
-54 + -5r + 3r2 = -4

Solving
-54 + -5r + 3r2 = -4

Solving for variable 'r'.

Reorder the terms:
-54 + 4 + -5r + 3r2 = -4 + 4

Combine like terms: -54 + 4 = -50
-50 + -5r + 3r2 = -4 + 4

Combine like terms: -4 + 4 = 0
-50 + -5r + 3r2 = 0

Factor a trinomial.
(-10 + -3r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-10 + -3r)' equal to zero and attempt to solve:

Simplifying
-10 + -3r = 0

Solving
-10 + -3r = 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 + -3r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3r = 0 + 10
-3r = 0 + 10

Combine like terms: 0 + 10 = 10
-3r = 10

Divide each side by '-3'.
r = -3.333333333

Simplifying
r = -3.333333333
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-3.333333333, 5}