(2z-1)(-z+3z-4)=

Solution for (2z-1)(-z+3z-4)= equation:

Simplifying
(2z + -1)(-1z + 3z + -4) = 0

Reorder the terms:
(-1 + 2z)(-1z + 3z + -4) = 0

Reorder the terms:
(-1 + 2z)(-4 + -1z + 3z) = 0

Combine like terms: -1z + 3z = 2z
(-1 + 2z)(-4 + 2z) = 0

Multiply (-1 + 2z) * (-4 + 2z)
(-1(-4 + 2z) + 2z * (-4 + 2z)) = 0
((-4 * -1 + 2z * -1) + 2z * (-4 + 2z)) = 0
((4 + -2z) + 2z * (-4 + 2z)) = 0
(4 + -2z + (-4 * 2z + 2z * 2z)) = 0
(4 + -2z + (-8z + 4z2)) = 0

Combine like terms: -2z + -8z = -10z
(4 + -10z + 4z2) = 0

Solving
4 + -10z + 4z2 = 0

Solving for variable 'z'.

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

Factor a trinomial.
2((1 + -2z)(2 + -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 '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

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