(4z+1)(8+z)=0

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Solution for (4z+1)(8+z)=0 equation:


Simplifying
(4z + 1)(8 + z) = 0

Reorder the terms:
(1 + 4z)(8 + z) = 0

Multiply (1 + 4z) * (8 + z)
(1(8 + z) + 4z * (8 + z)) = 0
((8 * 1 + z * 1) + 4z * (8 + z)) = 0
((8 + 1z) + 4z * (8 + z)) = 0
(8 + 1z + (8 * 4z + z * 4z)) = 0
(8 + 1z + (32z + 4z2)) = 0

Combine like terms: 1z + 32z = 33z
(8 + 33z + 4z2) = 0

Solving
8 + 33z + 4z2 = 0

Solving for variable 'z'.

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

Subproblem 1

Set the factor '(8 + z)' equal to zero and attempt to solve: Simplifying 8 + z = 0 Solving 8 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + z = 0 + -8 z = 0 + -8 Combine like terms: 0 + -8 = -8 z = -8 Simplifying z = -8

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 = {-8, -0.25}

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