3k^2+10k-41=7

Solution for 3k^2+10k-41=7 equation:

Simplifying
3k2 + 10k + -41 = 7

Reorder the terms:
-41 + 10k + 3k2 = 7

Solving
-41 + 10k + 3k2 = 7

Solving for variable 'k'.

Reorder the terms:
-41 + -7 + 10k + 3k2 = 7 + -7

Combine like terms: -41 + -7 = -48
-48 + 10k + 3k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-48 + 10k + 3k2 = 0

Factor a trinomial.
(-6 + -1k)(8 + -3k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {-6, 2.666666667}