(2k+1)x(k-4)=

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Solution for (2k+1)x(k-4)= equation: 


Simplifying
(2k + 1) * x(k + -4) = 0

Reorder the terms:
(1 + 2k) * x(k + -4) = 0

Reorder the terms:
(1 + 2k) * x(-4 + k) = 0

Reorder the terms for easier multiplication:
x(1 + 2k)(-4 + k) = 0

Multiply (1 + 2k) * (-4 + k)
x(1(-4 + k) + 2k * (-4 + k)) = 0
x((-4 * 1 + k * 1) + 2k * (-4 + k)) = 0
x((-4 + 1k) + 2k * (-4 + k)) = 0
x(-4 + 1k + (-4 * 2k + k * 2k)) = 0
x(-4 + 1k + (-8k + 2k2)) = 0

Combine like terms: 1k + -8k = -7k
x(-4 + -7k + 2k2) = 0
(-4 * x + -7k * x + 2k2 * x) = 0

Reorder the terms:
(-7kx + 2k2x + -4x) = 0
(-7kx + 2k2x + -4x) = 0

Solving
-7kx + 2k2x + -4x = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7k + 2k2 + -4) = 0

Factor a trinomial.
x((k + -4)(2k + 1)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
k + -4 = 0

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

Simplifying
2k + 1 = 0

Reorder the terms:
1 + 2k = 0

Solving
1 + 2k = 0

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

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

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

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

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Solution
k = {4, -0.5}

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