(4k-5)(k+7)=0

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Solution for (4k-5)(k+7)=0 equation: 


Simplifying
(4k + -5)(k + 7) = 0

Reorder the terms:
(-5 + 4k)(k + 7) = 0

Reorder the terms:
(-5 + 4k)(7 + k) = 0

Multiply (-5 + 4k) * (7 + k)
(-5(7 + k) + 4k * (7 + k)) = 0
((7 * -5 + k * -5) + 4k * (7 + k)) = 0
((-35 + -5k) + 4k * (7 + k)) = 0
(-35 + -5k + (7 * 4k + k * 4k)) = 0
(-35 + -5k + (28k + 4k2)) = 0

Combine like terms: -5k + 28k = 23k
(-35 + 23k + 4k2) = 0

Solving
-35 + 23k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -1k)(5 + -4k) = 0


Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve:

Simplifying
-7 + -1k = 0

Solving
-7 + -1k = 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 + -1k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1k = 0 + 7
-1k = 0 + 7

Combine like terms: 0 + 7 = 7
-1k = 7

Divide each side by '-1'.
k = -7

Simplifying
k = -7

Subproblem 2
Set the factor '(5 + -4k)' equal to zero and attempt to solve:

Simplifying
5 + -4k = 0

Solving
5 + -4k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4k = 0 + -5
-4k = 0 + -5

Combine like terms: 0 + -5 = -5
-4k = -5

Divide each side by '-4'.
k = 1.25

Simplifying
k = 1.25
Solution
k = {-7, 1.25}

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