(2k-7)(k-2)=0

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


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

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

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

Multiply (-7 + 2k) * (-2 + k)
(-7(-2 + k) + 2k * (-2 + k)) = 0
((-2 * -7 + k * -7) + 2k * (-2 + k)) = 0
((14 + -7k) + 2k * (-2 + k)) = 0
(14 + -7k + (-2 * 2k + k * 2k)) = 0
(14 + -7k + (-4k + 2k2)) = 0

Combine like terms: -7k + -4k = -11k
(14 + -11k + 2k2) = 0

Solving
14 + -11k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -1k)(7 + -2k) = 0


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

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2

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

Simplifying
7 + -2k = 0

Solving
7 + -2k = 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 + -2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5
Solution
k = {2, 3.5}

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