9r^2-5r-10=-6

Solution for 9r^2-5r-10=-6 equation:

Simplifying
9r2 + -5r + -10 = -6

Reorder the terms:
-10 + -5r + 9r2 = -6

Solving
-10 + -5r + 9r2 = -6

Solving for variable 'r'.

Reorder the terms:
-10 + 6 + -5r + 9r2 = -6 + 6

Combine like terms: -10 + 6 = -4
-4 + -5r + 9r2 = -6 + 6

Combine like terms: -6 + 6 = 0
-4 + -5r + 9r2 = 0

Factor a trinomial.
(-4 + -9r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -9r)' equal to zero and attempt to solve:

Simplifying
-4 + -9r = 0

Solving
-4 + -9r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9r = 0 + 4
-9r = 0 + 4

Combine like terms: 0 + 4 = 4
-9r = 4

Divide each side by '-9'.
r = -0.4444444444

Simplifying
r = -0.4444444444
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 = {-0.4444444444, 1}