(4r+9r)(r-6)=-(31r-186)

Solution for (4r+9r)(r-6)=-(31r-186) equation:

Simplifying
(4r + 9r)(r + -6) = -1(31r + -186)

Combine like terms: 4r + 9r = 13r
(13r)(r + -6) = -1(31r + -186)

Remove parenthesis around (13r)
13r(r + -6) = -1(31r + -186)

Reorder the terms:
13r(-6 + r) = -1(31r + -186)
(-6 * 13r + r * 13r) = -1(31r + -186)
(-78r + 13r2) = -1(31r + -186)

Reorder the terms:
-78r + 13r2 = -1(-186 + 31r)
-78r + 13r2 = (-186 * -1 + 31r * -1)
-78r + 13r2 = (186 + -31r)

Solving
-78r + 13r2 = 186 + -31r

Solving for variable 'r'.

Reorder the terms:
-186 + -78r + 31r + 13r2 = 186 + -31r + -186 + 31r

Combine like terms: -78r + 31r = -47r
-186 + -47r + 13r2 = 186 + -31r + -186 + 31r

Reorder the terms:
-186 + -47r + 13r2 = 186 + -186 + -31r + 31r

Combine like terms: 186 + -186 = 0
-186 + -47r + 13r2 = 0 + -31r + 31r
-186 + -47r + 13r2 = -31r + 31r

Combine like terms: -31r + 31r = 0
-186 + -47r + 13r2 = 0

Factor a trinomial.
(-31 + -13r)(6 + -1r) = 0

Subproblem 1
Set the factor '(-31 + -13r)' equal to zero and attempt to solve:

Simplifying
-31 + -13r = 0

Solving
-31 + -13r = 0

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

Add '31' to each side of the equation.
-31 + 31 + -13r = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -13r = 0 + 31
-13r = 0 + 31

Combine like terms: 0 + 31 = 31
-13r = 31

Divide each side by '-13'.
r = -2.384615385

Simplifying
r = -2.384615385
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 = {-2.384615385, 6}