4r^2+21r=18

Solution for 4r^2+21r=18 equation:

Simplifying
4r2 + 21r = 18

Reorder the terms:
21r + 4r2 = 18

Solving
21r + 4r2 = 18

Solving for variable 'r'.

Reorder the terms:
-18 + 21r + 4r2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 21r + 4r2 = 0

Factor a trinomial.
(-6 + -1r)(3 + -4r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4r = 0 + -3
-4r = 0 + -3

Combine like terms: 0 + -3 = -3
-4r = -3

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Solution
r = {-6, 0.75}