(-3k+7)(2k-8)=0

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Solution for (-3k+7)(2k-8)=0 equation: 


Simplifying
(-3k + 7)(2k + -8) = 0

Reorder the terms:
(7 + -3k)(2k + -8) = 0

Reorder the terms:
(7 + -3k)(-8 + 2k) = 0

Multiply (7 + -3k) * (-8 + 2k)
(7(-8 + 2k) + -3k * (-8 + 2k)) = 0
((-8 * 7 + 2k * 7) + -3k * (-8 + 2k)) = 0
((-56 + 14k) + -3k * (-8 + 2k)) = 0
(-56 + 14k + (-8 * -3k + 2k * -3k)) = 0
(-56 + 14k + (24k + -6k2)) = 0

Combine like terms: 14k + 24k = 38k
(-56 + 38k + -6k2) = 0

Solving
-56 + 38k + -6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 19k + -3k2) = 0

Factor a trinomial.
2((-4 + k)(7 + -3k)) = 0

Ignore the factor 2.

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

Simplifying
-4 + k = 0

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

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

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

Simplifying
k = 4

Subproblem 2
Set the factor '(7 + -3k)' equal to zero and attempt to solve:

Simplifying
7 + -3k = 0

Solving
7 + -3k = 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 + -3k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3k = 0 + -7
-3k = 0 + -7

Combine like terms: 0 + -7 = -7
-3k = -7

Divide each side by '-3'.
k = 2.333333333

Simplifying
k = 2.333333333
Solution
k = {4, 2.333333333}

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