(3k-8)(4k+3)=0

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Solution for (3k-8)(4k+3)=0 equation: 


Simplifying
(3k + -8)(4k + 3) = 0

Reorder the terms:
(-8 + 3k)(4k + 3) = 0

Reorder the terms:
(-8 + 3k)(3 + 4k) = 0

Multiply (-8 + 3k) * (3 + 4k)
(-8(3 + 4k) + 3k * (3 + 4k)) = 0
((3 * -8 + 4k * -8) + 3k * (3 + 4k)) = 0
((-24 + -32k) + 3k * (3 + 4k)) = 0
(-24 + -32k + (3 * 3k + 4k * 3k)) = 0
(-24 + -32k + (9k + 12k2)) = 0

Combine like terms: -32k + 9k = -23k
(-24 + -23k + 12k2) = 0

Solving
-24 + -23k + 12k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -4k)(8 + -3k) = 0


Subproblem 1
Set the factor '(-3 + -4k)' equal to zero and attempt to solve:

Simplifying
-3 + -4k = 0

Solving
-3 + -4k = 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 + -4k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4k = 0 + 3
-4k = 0 + 3

Combine like terms: 0 + 3 = 3
-4k = 3

Divide each side by '-4'.
k = -0.75

Simplifying
k = -0.75

Subproblem 2
Set the factor '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {-0.75, 2.666666667}

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