(2r+9)(r+10)=

Solution for (2r+9)(r+10)= equation:

Simplifying
(2r + 9)(r + 10) = 0

Reorder the terms:
(9 + 2r)(r + 10) = 0

Reorder the terms:
(9 + 2r)(10 + r) = 0

Multiply (9 + 2r) * (10 + r)
(9(10 + r) + 2r * (10 + r)) = 0
((10 * 9 + r * 9) + 2r * (10 + r)) = 0
((90 + 9r) + 2r * (10 + r)) = 0
(90 + 9r + (10 * 2r + r * 2r)) = 0
(90 + 9r + (20r + 2r2)) = 0

Combine like terms: 9r + 20r = 29r
(90 + 29r + 2r2) = 0

Solving
90 + 29r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(10 + r)(9 + 2r) = 0

Subproblem 1
Set the factor '(10 + r)' equal to zero and attempt to solve:

Simplifying
10 + r = 0

Solving
10 + r = 0

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

Add '-10' to each side of the equation.
10 + -10 + r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + r = 0 + -10
r = 0 + -10

Combine like terms: 0 + -10 = -10
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Solution
r = {-10, -4.5}