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

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


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

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

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

Combine like terms: 1z + 8z = 9z
(-2 + 9z + -4z2) = 0

Solving
-2 + 9z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + z)(1 + -4z) = 0

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 + -4z)' equal to zero and attempt to solve: Simplifying 1 + -4z = 0 Solving 1 + -4z = 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 + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4z = 0 + -1 -4z = 0 + -1 Combine like terms: 0 + -1 = -1 -4z = -1 Divide each side by '-4'. z = 0.25 Simplifying z = 0.25

Solution

z = {2, 0.25}

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