20((2+z)(1+2z))=0

Solution for 20((2+z)(1+2z))=0 equation:

Simplifying
20((2 + z)(1 + 2z)) = 0

Multiply (2 + z) * (1 + 2z)
20((2(1 + 2z) + z(1 + 2z))) = 0
20(((1 * 2 + 2z * 2) + z(1 + 2z))) = 0
20(((2 + 4z) + z(1 + 2z))) = 0
20((2 + 4z + (1 * z + 2z * z))) = 0
20((2 + 4z + (1z + 2z2))) = 0

Combine like terms: 4z + 1z = 5z
20((2 + 5z + 2z2)) = 0
(2 * 20 + 5z * 20 + 2z2 * 20) = 0
(40 + 100z + 40z2) = 0

Solving
40 + 100z + 40z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '20'.
20(2 + 5z + 2z2) = 0

Factor a trinomial.
20((2 + z)(1 + 2z)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

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

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

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

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

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

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

Simplifying
z = -0.5
Solution
z = {-2, -0.5}