(K-2)(4K+1)=0

Solution for (K-2)(4K+1)=0 equation:

Simplifying
(K + -2)(4K + 1) = 0

Reorder the terms:
(-2 + K)(4K + 1) = 0

Reorder the terms:
(-2 + K)(1 + 4K) = 0

Multiply (-2 + K) * (1 + 4K)
(-2(1 + 4K) + K(1 + 4K)) = 0
((1 * -2 + 4K * -2) + K(1 + 4K)) = 0
((-2 + -8K) + K(1 + 4K)) = 0
(-2 + -8K + (1 * K + 4K * K)) = 0
(-2 + -8K + (1K + 4K2)) = 0

Combine like terms: -8K + 1K = -7K
(-2 + -7K + 4K2) = 0

Solving
-2 + -7K + 4K2 = 0

Solving for variable 'K'.

Factor a trinomial.
(-1 + -4K)(2 + -1K) = 0

Subproblem 1
Set the factor '(-1 + -4K)' equal to zero and attempt to solve:

Simplifying
-1 + -4K = 0

Solving
-1 + -4K = 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 + -4K = 0 + 1

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

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

Divide each side by '-4'.
K = -0.25

Simplifying
K = -0.25
Subproblem 2
Set the factor '(2 + -1K)' equal to zero and attempt to solve:

Simplifying
2 + -1K = 0

Solving
2 + -1K = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1K = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1K = 0 + -2
-1K = 0 + -2

Combine like terms: 0 + -2 = -2
-1K = -2

Divide each side by '-1'.
K = 2

Simplifying
K = 2
Solution
K = {-0.25, 2}