-5k^2+8k+105=-7

Solution for -5k^2+8k+105=-7 equation:

Simplifying
-5k2 + 8k + 105 = -7

Reorder the terms:
105 + 8k + -5k2 = -7

Solving
105 + 8k + -5k2 = -7

Solving for variable 'k'.

Reorder the terms:
105 + 7 + 8k + -5k2 = -7 + 7

Combine like terms: 105 + 7 = 112
112 + 8k + -5k2 = -7 + 7

Combine like terms: -7 + 7 = 0
112 + 8k + -5k2 = 0

Factor a trinomial.
(28 + -5k)(4 + k) = 0

Subproblem 1
Set the factor '(28 + -5k)' equal to zero and attempt to solve:

Simplifying
28 + -5k = 0

Solving
28 + -5k = 0

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

Add '-28' to each side of the equation.
28 + -28 + -5k = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -5k = 0 + -28
-5k = 0 + -28

Combine like terms: 0 + -28 = -28
-5k = -28

Divide each side by '-5'.
k = 5.6

Simplifying
k = 5.6
Subproblem 2
Set the factor '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

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

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Solution
k = {5.6, -4}