(6-z)(4z-9)=0

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Solution for (6-z)(4z-9)=0 equation:


Simplifying
(6 + -1z)(4z + -9) = 0

Reorder the terms:
(6 + -1z)(-9 + 4z) = 0

Multiply (6 + -1z) * (-9 + 4z)
(6(-9 + 4z) + -1z * (-9 + 4z)) = 0
((-9 * 6 + 4z * 6) + -1z * (-9 + 4z)) = 0
((-54 + 24z) + -1z * (-9 + 4z)) = 0
(-54 + 24z + (-9 * -1z + 4z * -1z)) = 0
(-54 + 24z + (9z + -4z2)) = 0

Combine like terms: 24z + 9z = 33z
(-54 + 33z + -4z2) = 0

Solving
-54 + 33z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + z)(9 + -4z) = 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 '(9 + -4z)' equal to zero and attempt to solve: Simplifying 9 + -4z = 0 Solving 9 + -4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4z = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4z = 0 + -9 -4z = 0 + -9 Combine like terms: 0 + -9 = -9 -4z = -9 Divide each side by '-4'. z = 2.25 Simplifying z = 2.25

Solution

z = {6, 2.25}

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