2x(y-z)+x(y+x)=

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

Simplifying
2x(y + -1z) + x(y + x) = 0
(y * 2x + -1z * 2x) + x(y + x) = 0
(2xy + -2xz) + x(y + x) = 0

Reorder the terms:
2xy + -2xz + x(x + y) = 0
2xy + -2xz + (x * x + y * x) = 0

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

Reorder the terms:
2xy + xy + -2xz + x2 = 0

Combine like terms: 2xy + xy = 3xy
3xy + -2xz + x2 = 0

Solving
3xy + -2xz + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(3y + -2z + x) = 0

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 '(3y + -2z + x)' equal to zero and attempt to solve:

Simplifying
3y + -2z + x = 0

Reorder the terms:
x + 3y + -2z = 0

Solving
x + 3y + -2z = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y + -2z = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 + -2z = 0 + -3y
x + -2z = 0 + -3y
Remove the zero:
x + -2z = -3y

Add '2z' to each side of the equation.
x + -2z + 2z = -3y + 2z

Combine like terms: -2z + 2z = 0
x + 0 = -3y + 2z
x = -3y + 2z

Simplifying
x = -3y + 2z
Solution
x = {0, -3y + 2z}