(6-z)(3z-4)=0

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Solution for (6-z)(3z-4)=0 equation:


Simplifying
(6 + -1z)(3z + -4) = 0

Reorder the terms:
(6 + -1z)(-4 + 3z) = 0

Multiply (6 + -1z) * (-4 + 3z)
(6(-4 + 3z) + -1z * (-4 + 3z)) = 0
((-4 * 6 + 3z * 6) + -1z * (-4 + 3z)) = 0
((-24 + 18z) + -1z * (-4 + 3z)) = 0
(-24 + 18z + (-4 * -1z + 3z * -1z)) = 0
(-24 + 18z + (4z + -3z2)) = 0

Combine like terms: 18z + 4z = 22z
(-24 + 22z + -3z2) = 0

Solving
-24 + 22z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + z)(4 + -3z) = 0

Subproblem 1

Set the factor '(-6 + z)' equal to zero and attempt to solve: Simplifying -6 + z = 0 Solving -6 + z = 0 Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 0 + 6 Combine like terms: -6 + 6 = 0 0 + z = 0 + 6 z = 0 + 6 Combine like terms: 0 + 6 = 6 z = 6 Simplifying z = 6

Subproblem 2

Set the factor '(4 + -3z)' equal to zero and attempt to solve: Simplifying 4 + -3z = 0 Solving 4 + -3z = 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 + -3z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3z = 0 + -4 -3z = 0 + -4 Combine like terms: 0 + -4 = -4 -3z = -4 Divide each side by '-3'. z = 1.333333333 Simplifying z = 1.333333333

Solution

z = {6, 1.333333333}

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