(4K+5)(K-3)=0

Solution for (4K+5)(K-3)=0 equation:

Simplifying
(4K + 5)(K + -3) = 0

Reorder the terms:
(5 + 4K)(K + -3) = 0

Reorder the terms:
(5 + 4K)(-3 + K) = 0

Multiply (5 + 4K) * (-3 + K)
(5(-3 + K) + 4K * (-3 + K)) = 0
((-3 * 5 + K * 5) + 4K * (-3 + K)) = 0
((-15 + 5K) + 4K * (-3 + K)) = 0
(-15 + 5K + (-3 * 4K + K * 4K)) = 0
(-15 + 5K + (-12K + 4K2)) = 0

Combine like terms: 5K + -12K = -7K
(-15 + -7K + 4K2) = 0

Solving
-15 + -7K + 4K2 = 0

Solving for variable 'K'.

Factor a trinomial.
(-5 + -4K)(3 + -1K) = 0

Subproblem 1
Set the factor '(-5 + -4K)' equal to zero and attempt to solve:

Simplifying
-5 + -4K = 0

Solving
-5 + -4K = 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 + -4K = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4K = 0 + 5
-4K = 0 + 5

Combine like terms: 0 + 5 = 5
-4K = 5

Divide each side by '-4'.
K = -1.25

Simplifying
K = -1.25
Subproblem 2
Set the factor '(3 + -1K)' equal to zero and attempt to solve:

Simplifying
3 + -1K = 0

Solving
3 + -1K = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1K = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1K = 0 + -3
-1K = 0 + -3

Combine like terms: 0 + -3 = -3
-1K = -3

Divide each side by '-1'.
K = 3

Simplifying
K = 3
Solution
K = {-1.25, 3}