k(5k+4)+(10(k+1)-1)=

Solution for k(5k+4)+(10(k+1)-1)= equation:

Simplifying
k(5k + 4) + (10(k + 1) + -1) = 0

Reorder the terms:
k(4 + 5k) + (10(k + 1) + -1) = 0
(4 * k + 5k * k) + (10(k + 1) + -1) = 0
(4k + 5k2) + (10(k + 1) + -1) = 0

Reorder the terms:
4k + 5k2 + (10(1 + k) + -1) = 0
4k + 5k2 + ((1 * 10 + k * 10) + -1) = 0
4k + 5k2 + ((10 + 10k) + -1) = 0

Reorder the terms:
4k + 5k2 + (10 + -1 + 10k) = 0

Combine like terms: 10 + -1 = 9
4k + 5k2 + (9 + 10k) = 0

Remove parenthesis around (9 + 10k)
4k + 5k2 + 9 + 10k = 0

Reorder the terms:
9 + 4k + 10k + 5k2 = 0

Combine like terms: 4k + 10k = 14k
9 + 14k + 5k2 = 0

Solving
9 + 14k + 5k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(9 + 5k)(1 + k) = 0

Subproblem 1
Set the factor '(9 + 5k)' equal to zero and attempt to solve:

Simplifying
9 + 5k = 0

Solving
9 + 5k = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5k = 0 + -9
5k = 0 + -9

Combine like terms: 0 + -9 = -9
5k = -9

Divide each side by '5'.
k = -1.8

Simplifying
k = -1.8
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

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

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

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

Simplifying
k = -1
Solution
k = {-1.8, -1}