(8-z)(3z-2)=0

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Solution for (8-z)(3z-2)=0 equation:


Simplifying
(8 + -1z)(3z + -2) = 0

Reorder the terms:
(8 + -1z)(-2 + 3z) = 0

Multiply (8 + -1z) * (-2 + 3z)
(8(-2 + 3z) + -1z * (-2 + 3z)) = 0
((-2 * 8 + 3z * 8) + -1z * (-2 + 3z)) = 0
((-16 + 24z) + -1z * (-2 + 3z)) = 0
(-16 + 24z + (-2 * -1z + 3z * -1z)) = 0
(-16 + 24z + (2z + -3z2)) = 0

Combine like terms: 24z + 2z = 26z
(-16 + 26z + -3z2) = 0

Solving
-16 + 26z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + z)(2 + -3z) = 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 '(2 + -3z)' equal to zero and attempt to solve: Simplifying 2 + -3z = 0 Solving 2 + -3z = 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 + -3z = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3z = 0 + -2 -3z = 0 + -2 Combine like terms: 0 + -2 = -2 -3z = -2 Divide each side by '-3'. z = 0.6666666667 Simplifying z = 0.6666666667

Solution

z = {8, 0.6666666667}

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