(k-3)(k-2)+(2k+9)(k+9)=k(2k+24)+150

Solution for (k-3)(k-2)+(2k+9)(k+9)=k(2k+24)+150 equation:

Simplifying
(k + -3)(k + -2) + (2k + 9)(k + 9) = k(2k + 24) + 150

Reorder the terms:
(-3 + k)(k + -2) + (2k + 9)(k + 9) = k(2k + 24) + 150

Reorder the terms:
(-3 + k)(-2 + k) + (2k + 9)(k + 9) = k(2k + 24) + 150

Multiply (-3 + k) * (-2 + k)
(-3(-2 + k) + k(-2 + k)) + (2k + 9)(k + 9) = k(2k + 24) + 150
((-2 * -3 + k * -3) + k(-2 + k)) + (2k + 9)(k + 9) = k(2k + 24) + 150
((6 + -3k) + k(-2 + k)) + (2k + 9)(k + 9) = k(2k + 24) + 150
(6 + -3k + (-2 * k + k * k)) + (2k + 9)(k + 9) = k(2k + 24) + 150
(6 + -3k + (-2k + k2)) + (2k + 9)(k + 9) = k(2k + 24) + 150

Combine like terms: -3k + -2k = -5k
(6 + -5k + k2) + (2k + 9)(k + 9) = k(2k + 24) + 150

Reorder the terms:
6 + -5k + k2 + (9 + 2k)(k + 9) = k(2k + 24) + 150

Reorder the terms:
6 + -5k + k2 + (9 + 2k)(9 + k) = k(2k + 24) + 150

Multiply (9 + 2k) * (9 + k)
6 + -5k + k2 + (9(9 + k) + 2k * (9 + k)) = k(2k + 24) + 150
6 + -5k + k2 + ((9 * 9 + k * 9) + 2k * (9 + k)) = k(2k + 24) + 150
6 + -5k + k2 + ((81 + 9k) + 2k * (9 + k)) = k(2k + 24) + 150
6 + -5k + k2 + (81 + 9k + (9 * 2k + k * 2k)) = k(2k + 24) + 150
6 + -5k + k2 + (81 + 9k + (18k + 2k2)) = k(2k + 24) + 150

Combine like terms: 9k + 18k = 27k
6 + -5k + k2 + (81 + 27k + 2k2) = k(2k + 24) + 150

Reorder the terms:
6 + 81 + -5k + 27k + k2 + 2k2 = k(2k + 24) + 150

Combine like terms: 6 + 81 = 87
87 + -5k + 27k + k2 + 2k2 = k(2k + 24) + 150

Combine like terms: -5k + 27k = 22k
87 + 22k + k2 + 2k2 = k(2k + 24) + 150

Combine like terms: k2 + 2k2 = 3k2
87 + 22k + 3k2 = k(2k + 24) + 150

Reorder the terms:
87 + 22k + 3k2 = k(24 + 2k) + 150
87 + 22k + 3k2 = (24 * k + 2k * k) + 150
87 + 22k + 3k2 = (24k + 2k2) + 150

Reorder the terms:
87 + 22k + 3k2 = 150 + 24k + 2k2

Solving
87 + 22k + 3k2 = 150 + 24k + 2k2

Solving for variable 'k'.

Reorder the terms:
87 + -150 + 22k + -24k + 3k2 + -2k2 = 150 + 24k + 2k2 + -150 + -24k + -2k2

Combine like terms: 87 + -150 = -63
-63 + 22k + -24k + 3k2 + -2k2 = 150 + 24k + 2k2 + -150 + -24k + -2k2

Combine like terms: 22k + -24k = -2k
-63 + -2k + 3k2 + -2k2 = 150 + 24k + 2k2 + -150 + -24k + -2k2

Combine like terms: 3k2 + -2k2 = 1k2
-63 + -2k + 1k2 = 150 + 24k + 2k2 + -150 + -24k + -2k2

Reorder the terms:
-63 + -2k + 1k2 = 150 + -150 + 24k + -24k + 2k2 + -2k2

Combine like terms: 150 + -150 = 0
-63 + -2k + 1k2 = 0 + 24k + -24k + 2k2 + -2k2
-63 + -2k + 1k2 = 24k + -24k + 2k2 + -2k2

Combine like terms: 24k + -24k = 0
-63 + -2k + 1k2 = 0 + 2k2 + -2k2
-63 + -2k + 1k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
-63 + -2k + 1k2 = 0

Factor a trinomial.
(-7 + -1k)(9 + -1k) = 0

Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve:

Simplifying
-7 + -1k = 0

Solving
-7 + -1k = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1k = 0 + 7
-1k = 0 + 7

Combine like terms: 0 + 7 = 7
-1k = 7

Divide each side by '-1'.
k = -7

Simplifying
k = -7
Subproblem 2
Set the factor '(9 + -1k)' equal to zero and attempt to solve:

Simplifying
9 + -1k = 0

Solving
9 + -1k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1k = 0 + -9
-1k = 0 + -9

Combine like terms: 0 + -9 = -9
-1k = -9

Divide each side by '-1'.
k = 9

Simplifying
k = 9
Solution
k = {-7, 9}