(5+5)*[2y(z+1)]=

Solution for (5+5)*[2y(z+1)]= equation:

Simplifying
(5 + 5)[2y(z + 1)] = 0

Combine like terms: 5 + 5 = 10
(10)[2y(z + 1)] = 0

Reorder the terms:
10[2y(1 + z)] = 0
10[(1 * 2y + z * 2y)] = 0
10[(2y + 2yz)] = 0
[2y * 10 + 2yz * 10] = 0
[20y + 20yz] = 0

Solving
20y + 20yz = 0

Solving for variable 'y'.

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

Factor out the Greatest Common Factor (GCF), '20y'.
20y(1 + z) = 0

Ignore the factor 20.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

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

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

Simplifying
0 = -1 + -1z

The solution to this equation could not be determined.

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