(k^2)-(4)=1.5k(2)

Solution for (k^2)-(4)=1.5k(2) equation:

Simplifying
(k2) + -1(4) = 1.5k(2)
k2 + -1(4) = 1.5k(2)

Multiply -1 * 4
k2 + -4 = 1.5k(2)

Reorder the terms:
-4 + k2 = 1.5k(2)

Reorder the terms for easier multiplication:
-4 + k2 = 1.5 * 2k

Multiply 1.5 * 2
-4 + k2 = 3k

Solving
-4 + k2 = 3k

Solving for variable 'k'.

Reorder the terms:
-4 + -3k + k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-4 + -3k + k2 = 0

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

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

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 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 + -1k = 0 + 1

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

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

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

Simplifying
k = -1
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 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 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-1, 4}