=2x(x+5y+4z)

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Solution for =2x(x+5y+4z) equation: 


Simplifying
0 = 2x(x + 5y + 4z)
0 = (x * 2x + 5y * 2x + 4z * 2x)

Reorder the terms:
0 = (10xy + 8xz + 2x2)
0 = (10xy + 8xz + 2x2)

Solving
0 = 10xy + 8xz + 2x2

Solving for variable 'x'.
Remove the zero:
-10xy + -8xz + -2x2 = 10xy + 8xz + 2x2 + -10xy + -8xz + -2x2

Reorder the terms:
-10xy + -8xz + -2x2 = 10xy + -10xy + 8xz + -8xz + 2x2 + -2x2

Combine like terms: 10xy + -10xy = 0
-10xy + -8xz + -2x2 = 0 + 8xz + -8xz + 2x2 + -2x2
-10xy + -8xz + -2x2 = 8xz + -8xz + 2x2 + -2x2

Combine like terms: 8xz + -8xz = 0
-10xy + -8xz + -2x2 = 0 + 2x2 + -2x2
-10xy + -8xz + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10xy + -8xz + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(5y + 4z + x) = 0

Ignore the factor -2.

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 '(5y + 4z + x)' equal to zero and attempt to solve:

Simplifying
5y + 4z + x = 0

Reorder the terms:
x + 5y + 4z = 0

Solving
x + 5y + 4z = 0

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

Add '-5y' to each side of the equation.
x + 5y + -5y + 4z = 0 + -5y

Combine like terms: 5y + -5y = 0
x + 0 + 4z = 0 + -5y
x + 4z = 0 + -5y
Remove the zero:
x + 4z = -5y

Add '-4z' to each side of the equation.
x + 4z + -4z = -5y + -4z

Combine like terms: 4z + -4z = 0
x + 0 = -5y + -4z
x = -5y + -4z

Simplifying
x = -5y + -4z
Solution
x = {0, -5y + -4z}

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