(6k+9)(4k-11)=0

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Solution for (6k+9)(4k-11)=0 equation: 


Simplifying
(6k + 9)(4k + -11) = 0

Reorder the terms:
(9 + 6k)(4k + -11) = 0

Reorder the terms:
(9 + 6k)(-11 + 4k) = 0

Multiply (9 + 6k) * (-11 + 4k)
(9(-11 + 4k) + 6k * (-11 + 4k)) = 0
((-11 * 9 + 4k * 9) + 6k * (-11 + 4k)) = 0
((-99 + 36k) + 6k * (-11 + 4k)) = 0
(-99 + 36k + (-11 * 6k + 4k * 6k)) = 0
(-99 + 36k + (-66k + 24k2)) = 0

Combine like terms: 36k + -66k = -30k
(-99 + -30k + 24k2) = 0

Solving
-99 + -30k + 24k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + -10k + 8k2) = 0

Factor a trinomial.
3((-3 + -2k)(11 + -4k)) = 0

Ignore the factor 3.

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

Simplifying
-3 + -2k = 0

Solving
-3 + -2k = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2k = 0 + 3

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

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

Divide each side by '-2'.
k = -1.5

Simplifying
k = -1.5

Subproblem 2
Set the factor '(11 + -4k)' equal to zero and attempt to solve:

Simplifying
11 + -4k = 0

Solving
11 + -4k = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4k = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4k = 0 + -11
-4k = 0 + -11

Combine like terms: 0 + -11 = -11
-4k = -11

Divide each side by '-4'.
k = 2.75

Simplifying
k = 2.75
Solution
k = {-1.5, 2.75}

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