(2k+2)(9k+5)=

Solution for (2k+2)(9k+5)= equation:

Simplifying
(2k + 2)(9k + 5) = 0

Reorder the terms:
(2 + 2k)(9k + 5) = 0

Reorder the terms:
(2 + 2k)(5 + 9k) = 0

Multiply (2 + 2k) * (5 + 9k)
(2(5 + 9k) + 2k * (5 + 9k)) = 0
((5 * 2 + 9k * 2) + 2k * (5 + 9k)) = 0
((10 + 18k) + 2k * (5 + 9k)) = 0
(10 + 18k + (5 * 2k + 9k * 2k)) = 0
(10 + 18k + (10k + 18k2)) = 0

Combine like terms: 18k + 10k = 28k
(10 + 28k + 18k2) = 0

Solving
10 + 28k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 14k + 9k2) = 0

Factor a trinomial.
2((1 + k)(5 + 9k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(5 + 9k)' equal to zero and attempt to solve:

Simplifying
5 + 9k = 0

Solving
5 + 9k = 0

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

Add '-5' to each side of the equation.
5 + -5 + 9k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9k = 0 + -5
9k = 0 + -5

Combine like terms: 0 + -5 = -5
9k = -5

Divide each side by '9'.
k = -0.5555555556

Simplifying
k = -0.5555555556
Solution
k = {-1, -0.5555555556}