18k^2=84k+144

Solution for 18k^2=84k+144 equation:

Simplifying
18k2 = 84k + 144

Reorder the terms:
18k2 = 144 + 84k

Solving
18k2 = 144 + 84k

Solving for variable 'k'.

Reorder the terms:
-144 + -84k + 18k2 = 144 + 84k + -144 + -84k

Reorder the terms:
-144 + -84k + 18k2 = 144 + -144 + 84k + -84k

Combine like terms: 144 + -144 = 0
-144 + -84k + 18k2 = 0 + 84k + -84k
-144 + -84k + 18k2 = 84k + -84k

Combine like terms: 84k + -84k = 0
-144 + -84k + 18k2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-24 + -14k + 3k2) = 0

Factor a trinomial.
6((-4 + -3k)(6 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-4 + -3k)' equal to zero and attempt to solve:

Simplifying
-4 + -3k = 0

Solving
-4 + -3k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3k = 0 + 4
-3k = 0 + 4

Combine like terms: 0 + 4 = 4
-3k = 4

Divide each side by '-3'.
k = -1.333333333

Simplifying
k = -1.333333333
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-1.333333333, 6}