3k^2=42-15k

Solution for 3k^2=42-15k equation:

Simplifying
3k2 = 42 + -15k

Solving
3k2 = 42 + -15k

Solving for variable 'k'.

Reorder the terms:
-42 + 15k + 3k2 = 42 + -15k + -42 + 15k

Reorder the terms:
-42 + 15k + 3k2 = 42 + -42 + -15k + 15k

Combine like terms: 42 + -42 = 0
-42 + 15k + 3k2 = 0 + -15k + 15k
-42 + 15k + 3k2 = -15k + 15k

Combine like terms: -15k + 15k = 0
-42 + 15k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5k + k2) = 0

Factor a trinomial.
3((-7 + -1k)(2 + -1k)) = 0

Ignore the factor 3.
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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-7, 2}