8r^2-6=18r-1

Solution for 8r^2-6=18r-1 equation:

Simplifying
8r2 + -6 = 18r + -1

Reorder the terms:
-6 + 8r2 = 18r + -1

Reorder the terms:
-6 + 8r2 = -1 + 18r

Solving
-6 + 8r2 = -1 + 18r

Solving for variable 'r'.

Reorder the terms:
-6 + 1 + -18r + 8r2 = -1 + 18r + 1 + -18r

Combine like terms: -6 + 1 = -5
-5 + -18r + 8r2 = -1 + 18r + 1 + -18r

Reorder the terms:
-5 + -18r + 8r2 = -1 + 1 + 18r + -18r

Combine like terms: -1 + 1 = 0
-5 + -18r + 8r2 = 0 + 18r + -18r
-5 + -18r + 8r2 = 18r + -18r

Combine like terms: 18r + -18r = 0
-5 + -18r + 8r2 = 0

Factor a trinomial.
(-1 + -4r)(5 + -2r) = 0

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

Simplifying
-1 + -4r = 0

Solving
-1 + -4r = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4r = 0 + 1

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

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

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

Simplifying
r = -0.25
Subproblem 2
Set the factor '(5 + -2r)' equal to zero and attempt to solve:

Simplifying
5 + -2r = 0

Solving
5 + -2r = 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 + -2r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2r = 0 + -5
-2r = 0 + -5

Combine like terms: 0 + -5 = -5
-2r = -5

Divide each side by '-2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {-0.25, 2.5}