5(10k+1)2(2+8k)=

Solution for 5(10k+1)2(2+8k)= equation:

Simplifying
5(10k + 1) * 2(2 + 8k) = 0

Reorder the terms:
5(1 + 10k) * 2(2 + 8k) = 0

Reorder the terms for easier multiplication:
5 * 2(1 + 10k)(2 + 8k) = 0

Multiply 5 * 2
10(1 + 10k)(2 + 8k) = 0

Multiply (1 + 10k) * (2 + 8k)
10(1(2 + 8k) + 10k * (2 + 8k)) = 0
10((2 * 1 + 8k * 1) + 10k * (2 + 8k)) = 0
10((2 + 8k) + 10k * (2 + 8k)) = 0
10(2 + 8k + (2 * 10k + 8k * 10k)) = 0
10(2 + 8k + (20k + 80k2)) = 0

Combine like terms: 8k + 20k = 28k
10(2 + 28k + 80k2) = 0
(2 * 10 + 28k * 10 + 80k2 * 10) = 0
(20 + 280k + 800k2) = 0

Solving
20 + 280k + 800k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '20'.
20(1 + 14k + 40k2) = 0

Factor a trinomial.
20((1 + 4k)(1 + 10k)) = 0

Ignore the factor 20.
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 '(1 + 10k)' equal to zero and attempt to solve:

Simplifying
1 + 10k = 0

Solving
1 + 10k = 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 + 10k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10k = 0 + -1
10k = 0 + -1

Combine like terms: 0 + -1 = -1
10k = -1

Divide each side by '10'.
k = -0.1

Simplifying
k = -0.1
Solution
k = {-0.25, -0.1}