r^2+9r-4=2+4r

Solution for r^2+9r-4=2+4r equation:

Simplifying
r2 + 9r + -4 = 2 + 4r

Reorder the terms:
-4 + 9r + r2 = 2 + 4r

Solving
-4 + 9r + r2 = 2 + 4r

Solving for variable 'r'.

Reorder the terms:
-4 + -2 + 9r + -4r + r2 = 2 + 4r + -2 + -4r

Combine like terms: -4 + -2 = -6
-6 + 9r + -4r + r2 = 2 + 4r + -2 + -4r

Combine like terms: 9r + -4r = 5r
-6 + 5r + r2 = 2 + 4r + -2 + -4r

Reorder the terms:
-6 + 5r + r2 = 2 + -2 + 4r + -4r

Combine like terms: 2 + -2 = 0
-6 + 5r + r2 = 0 + 4r + -4r
-6 + 5r + r2 = 4r + -4r

Combine like terms: 4r + -4r = 0
-6 + 5r + r2 = 0

Factor a trinomial.
(-6 + -1r)(1 + -1r) = 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 '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

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

Simplifying
r = 1
Solution
r = {-6, 1}