(2k+4)(2k+9)=3k^2+11

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Solution for (2k+4)(2k+9)=3k^2+11 equation: 


Simplifying
(2k + 4)(2k + 9) = 3k2 + 11

Reorder the terms:
(4 + 2k)(2k + 9) = 3k2 + 11

Reorder the terms:
(4 + 2k)(9 + 2k) = 3k2 + 11

Multiply (4 + 2k) * (9 + 2k)
(4(9 + 2k) + 2k * (9 + 2k)) = 3k2 + 11
((9 * 4 + 2k * 4) + 2k * (9 + 2k)) = 3k2 + 11
((36 + 8k) + 2k * (9 + 2k)) = 3k2 + 11
(36 + 8k + (9 * 2k + 2k * 2k)) = 3k2 + 11
(36 + 8k + (18k + 4k2)) = 3k2 + 11

Combine like terms: 8k + 18k = 26k
(36 + 26k + 4k2) = 3k2 + 11

Reorder the terms:
36 + 26k + 4k2 = 11 + 3k2

Solving
36 + 26k + 4k2 = 11 + 3k2

Solving for variable 'k'.

Reorder the terms:
36 + -11 + 26k + 4k2 + -3k2 = 11 + 3k2 + -11 + -3k2

Combine like terms: 36 + -11 = 25
25 + 26k + 4k2 + -3k2 = 11 + 3k2 + -11 + -3k2

Combine like terms: 4k2 + -3k2 = 1k2
25 + 26k + 1k2 = 11 + 3k2 + -11 + -3k2

Reorder the terms:
25 + 26k + 1k2 = 11 + -11 + 3k2 + -3k2

Combine like terms: 11 + -11 = 0
25 + 26k + 1k2 = 0 + 3k2 + -3k2
25 + 26k + 1k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
25 + 26k + 1k2 = 0

Factor a trinomial.
(25 + k)(1 + k) = 0


Subproblem 1
Set the factor '(25 + k)' equal to zero and attempt to solve:

Simplifying
25 + k = 0

Solving
25 + k = 0

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

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

Combine like terms: 25 + -25 = 0
0 + k = 0 + -25
k = 0 + -25

Combine like terms: 0 + -25 = -25
k = -25

Simplifying
k = -25

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

Simplifying
1 + k = 0

Solving
1 + k = 0

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

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

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

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

Simplifying
k = -1
Solution
k = {-25, -1}

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