16k^2-4(k+3)(5-4k)=0

Solution for 16k^2-4(k+3)(5-4k)=0 equation:

Simplifying
16k2 + -4(k + 3)(5 + -4k) = 0

Reorder the terms:
16k2 + -4(3 + k)(5 + -4k) = 0

Multiply (3 + k) * (5 + -4k)
16k2 + -4(3(5 + -4k) + k(5 + -4k)) = 0
16k2 + -4((5 * 3 + -4k * 3) + k(5 + -4k)) = 0
16k2 + -4((15 + -12k) + k(5 + -4k)) = 0
16k2 + -4(15 + -12k + (5 * k + -4k * k)) = 0
16k2 + -4(15 + -12k + (5k + -4k2)) = 0

Combine like terms: -12k + 5k = -7k
16k2 + -4(15 + -7k + -4k2) = 0
16k2 + (15 * -4 + -7k * -4 + -4k2 * -4) = 0
16k2 + (-60 + 28k + 16k2) = 0

Reorder the terms:
-60 + 28k + 16k2 + 16k2 = 0

Combine like terms: 16k2 + 16k2 = 32k2
-60 + 28k + 32k2 = 0

Solving
-60 + 28k + 32k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 7k + 8k2) = 0

Factor a trinomial.
4((-15 + -8k)(1 + -1k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-15 + -8k)' equal to zero and attempt to solve:

Simplifying
-15 + -8k = 0

Solving
-15 + -8k = 0

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

Add '15' to each side of the equation.
-15 + 15 + -8k = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8k = 0 + 15
-8k = 0 + 15

Combine like terms: 0 + 15 = 15
-8k = 15

Divide each side by '-8'.
k = -1.875

Simplifying
k = -1.875
Subproblem 2
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
Solution
k = {-1.875, 1}