k^2-31-2k+6+3k^2+2k=0

Solution for k^2-31-2k+6+3k^2+2k=0 equation:

Simplifying
k2 + -31 + -2k + 6 + 3k2 + 2k = 0

Reorder the terms:
-31 + 6 + -2k + 2k + k2 + 3k2 = 0

Combine like terms: -31 + 6 = -25
-25 + -2k + 2k + k2 + 3k2 = 0

Combine like terms: -2k + 2k = 0
-25 + 0 + k2 + 3k2 = 0
-25 + k2 + 3k2 = 0

Combine like terms: k2 + 3k2 = 4k2
-25 + 4k2 = 0

Solving
-25 + 4k2 = 0

Solving for variable 'k'.

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

Add '25' to each side of the equation.
-25 + 25 + 4k2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 4k2 = 0 + 25
4k2 = 0 + 25

Combine like terms: 0 + 25 = 25
4k2 = 25

Divide each side by '4'.
k2 = 6.25

Simplifying
k2 = 6.25

Take the square root of each side:
k = {-2.5, 2.5}