(z-1)(4z+2)=0

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

Simplifying
(z + -1)(4z + 2) = 0

Reorder the terms:
(-1 + z)(4z + 2) = 0

Reorder the terms:
(-1 + z)(2 + 4z) = 0

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

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

Solving
-2 + -2z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1z + 2z2) = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 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 + -1z = 0 + -1

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

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

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

Simplifying
z = 1
Solution
z = {-0.5, 1}