(4-z)(3z+8)=0

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Solution for (4-z)(3z+8)=0 equation:


Simplifying
(4 + -1z)(3z + 8) = 0

Reorder the terms:
(4 + -1z)(8 + 3z) = 0

Multiply (4 + -1z) * (8 + 3z)
(4(8 + 3z) + -1z * (8 + 3z)) = 0
((8 * 4 + 3z * 4) + -1z * (8 + 3z)) = 0
((32 + 12z) + -1z * (8 + 3z)) = 0
(32 + 12z + (8 * -1z + 3z * -1z)) = 0
(32 + 12z + (-8z + -3z2)) = 0

Combine like terms: 12z + -8z = 4z
(32 + 4z + -3z2) = 0

Solving
32 + 4z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + -1z)(8 + 3z) = 0

Subproblem 1

Set the factor '(4 + -1z)' equal to zero and attempt to solve: Simplifying 4 + -1z = 0 Solving 4 + -1z = 0 Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1z = 0 + -4 -1z = 0 + -4 Combine like terms: 0 + -4 = -4 -1z = -4 Divide each side by '-1'. z = 4 Simplifying z = 4

Subproblem 2

Set the factor '(8 + 3z)' equal to zero and attempt to solve: Simplifying 8 + 3z = 0 Solving 8 + 3z = 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 + 3z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3z = 0 + -8 3z = 0 + -8 Combine like terms: 0 + -8 = -8 3z = -8 Divide each side by '3'. z = -2.666666667 Simplifying z = -2.666666667

Solution

z = {4, -2.666666667}

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