k^2+-10k+35=7k+-35

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Solution for k^2+-10k+35=7k+-35 equation: 


Simplifying
k2 + -10k + 35 = 7k + -35

Reorder the terms:
35 + -10k + k2 = 7k + -35

Reorder the terms:
35 + -10k + k2 = -35 + 7k

Solving
35 + -10k + k2 = -35 + 7k

Solving for variable 'k'.

Reorder the terms:
35 + 35 + -10k + -7k + k2 = -35 + 7k + 35 + -7k

Combine like terms: 35 + 35 = 70
70 + -10k + -7k + k2 = -35 + 7k + 35 + -7k

Combine like terms: -10k + -7k = -17k
70 + -17k + k2 = -35 + 7k + 35 + -7k

Reorder the terms:
70 + -17k + k2 = -35 + 35 + 7k + -7k

Combine like terms: -35 + 35 = 0
70 + -17k + k2 = 0 + 7k + -7k
70 + -17k + k2 = 7k + -7k

Combine like terms: 7k + -7k = 0
70 + -17k + k2 = 0

Factor a trinomial.
(7 + -1k)(10 + -1k) = 0


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

Simplifying
7 + -1k = 0

Solving
7 + -1k = 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 + -1k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 0 + -7
-1k = 0 + -7

Combine like terms: 0 + -7 = -7
-1k = -7

Divide each side by '-1'.
k = 7

Simplifying
k = 7

Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {7, 10}

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