(1[4z-2]1)(1[9+z]1)=0

Solution for (1[4z-2]1)(1[9+z]1)=0 equation:

Simplifying
(1[4z + -2] * 1)(1[9 + z] * 1) = 0

Reorder the terms:
(1[-2 + 4z] * 1)(1[9 + z] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[-2 + 4z])(1[9 + z] * 1) = 0

Multiply 1 * 1
(1[-2 + 4z])(1[9 + z] * 1) = 0
([-2 * 1 + 4z * 1])(1[9 + z] * 1) = 0
([-2 + 4z])(1[9 + z] * 1) = 0

Reorder the terms for easier multiplication:
(-2 + 4z)(1 * 1[9 + z]) = 0

Multiply 1 * 1
(-2 + 4z)(1[9 + z]) = 0
(-2 + 4z)([9 * 1 + z * 1]) = 0
(-2 + 4z)([9 + 1z]) = 0

Multiply (-2 + 4z) * (9 + 1z)
(-2(9 + 1z) + 4z * (9 + 1z)) = 0
((9 * -2 + 1z * -2) + 4z * (9 + 1z)) = 0
((-18 + -2z) + 4z * (9 + 1z)) = 0
(-18 + -2z + (9 * 4z + 1z * 4z)) = 0
(-18 + -2z + (36z + 4z2)) = 0

Combine like terms: -2z + 36z = 34z
(-18 + 34z + 4z2) = 0

Solving
-18 + 34z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 17z + 2z2) = 0

Factor a trinomial.
2((-9 + -1z)(1 + -2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9
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 = {-9, 0.5}