10X(2-z)=4X(z-9)

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Solution for 10X(2-z)=4X(z-9) equation: 


Simplifying
10X(2 + -1z) = 4X(z + -9)
(2 * 10X + -1z * 10X) = 4X(z + -9)
(20X + -10zX) = 4X(z + -9)

Reorder the terms:
20X + -10zX = 4X(-9 + z)
20X + -10zX = (-9 * 4X + z * 4X)
20X + -10zX = (-36X + 4zX)

Solving
20X + -10zX = -36X + 4zX

Solving for variable 'X'.

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

Add '36X' to each side of the equation.
20X + 36X + -10zX = -36X + 36X + 4zX

Combine like terms: 20X + 36X = 56X
56X + -10zX = -36X + 36X + 4zX

Combine like terms: -36X + 36X = 0
56X + -10zX = 0 + 4zX
56X + -10zX = 4zX

Add '-4zX' to each side of the equation.
56X + -10zX + -4zX = 4zX + -4zX

Combine like terms: -10zX + -4zX = -14zX
56X + -14zX = 4zX + -4zX

Combine like terms: 4zX + -4zX = 0
56X + -14zX = 0

Factor out the Greatest Common Factor (GCF), '14X'.
14X(4 + -1z) = 0

Ignore the factor 14.

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

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0

Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Add 'z' to each side of the equation.
-1z + z = -4 + z

Combine like terms: -1z + z = 0
0 = -4 + z

Simplifying
0 = -4 + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}

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