0=k*k-12k+35

Solution for 0=k*k-12k+35 equation:

Simplifying
0 = k * k + -12k + 35

Multiply k * k
0 = k2 + -12k + 35

Reorder the terms:
0 = 35 + -12k + k2

Solving
0 = 35 + -12k + k2

Solving for variable 'k'.

Combine like terms: 0 + -35 = -35
-35 + 12k + -1k2 = 35 + -12k + k2 + -35 + 12k + -1k2

Reorder the terms:
-35 + 12k + -1k2 = 35 + -35 + -12k + 12k + k2 + -1k2

Combine like terms: 35 + -35 = 0
-35 + 12k + -1k2 = 0 + -12k + 12k + k2 + -1k2
-35 + 12k + -1k2 = -12k + 12k + k2 + -1k2

Combine like terms: -12k + 12k = 0
-35 + 12k + -1k2 = 0 + k2 + -1k2
-35 + 12k + -1k2 = k2 + -1k2

Combine like terms: k2 + -1k2 = 0
-35 + 12k + -1k2 = 0

Factor a trinomial.
(-7 + k)(5 + -1k) = 0

Subproblem 1
Set the factor '(-7 + k)' equal to zero and attempt to solve:

Simplifying
-7 + k = 0

Solving
-7 + k = 0

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

Add '7' to each side of the equation.
-7 + 7 + k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + k = 0 + 7
k = 0 + 7

Combine like terms: 0 + 7 = 7
k = 7

Simplifying
k = 7
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {7, 5}