(k^2+3k+3k+9)-(4k^2-2k-2k+1)=0

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Solution for (k^2+3k+3k+9)-(4k^2-2k-2k+1)=0 equation: 


Simplifying
(k2 + 3k + 3k + 9) + -1(4k2 + -2k + -2k + 1) = 0

Reorder the terms:
(9 + 3k + 3k + k2) + -1(4k2 + -2k + -2k + 1) = 0

Combine like terms: 3k + 3k = 6k
(9 + 6k + k2) + -1(4k2 + -2k + -2k + 1) = 0

Remove parenthesis around (9 + 6k + k2)
9 + 6k + k2 + -1(4k2 + -2k + -2k + 1) = 0

Reorder the terms:
9 + 6k + k2 + -1(1 + -2k + -2k + 4k2) = 0

Combine like terms: -2k + -2k = -4k
9 + 6k + k2 + -1(1 + -4k + 4k2) = 0
9 + 6k + k2 + (1 * -1 + -4k * -1 + 4k2 * -1) = 0
9 + 6k + k2 + (-1 + 4k + -4k2) = 0

Reorder the terms:
9 + -1 + 6k + 4k + k2 + -4k2 = 0

Combine like terms: 9 + -1 = 8
8 + 6k + 4k + k2 + -4k2 = 0

Combine like terms: 6k + 4k = 10k
8 + 10k + k2 + -4k2 = 0

Combine like terms: k2 + -4k2 = -3k2
8 + 10k + -3k2 = 0

Solving
8 + 10k + -3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + -1k)(2 + 3k) = 0


Subproblem 1
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4

Subproblem 2
Set the factor '(2 + 3k)' equal to zero and attempt to solve:

Simplifying
2 + 3k = 0

Solving
2 + 3k = 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 + 3k = 0 + -2

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

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

Divide each side by '3'.
k = -0.6666666667

Simplifying
k = -0.6666666667
Solution
k = {4, -0.6666666667}

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