(5z-4)(9-z)=0

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Solution for (5z-4)(9-z)=0 equation:


Simplifying
(5z + -4)(9 + -1z) = 0

Reorder the terms:
(-4 + 5z)(9 + -1z) = 0

Multiply (-4 + 5z) * (9 + -1z)
(-4(9 + -1z) + 5z * (9 + -1z)) = 0
((9 * -4 + -1z * -4) + 5z * (9 + -1z)) = 0
((-36 + 4z) + 5z * (9 + -1z)) = 0
(-36 + 4z + (9 * 5z + -1z * 5z)) = 0
(-36 + 4z + (45z + -5z2)) = 0

Combine like terms: 4z + 45z = 49z
(-36 + 49z + -5z2) = 0

Solving
-36 + 49z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + z)(4 + -5z) = 0

Subproblem 1

Set the factor '(-9 + z)' equal to zero and attempt to solve: Simplifying -9 + z = 0 Solving -9 + z = 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 + z = 0 + 9 Combine like terms: -9 + 9 = 0 0 + z = 0 + 9 z = 0 + 9 Combine like terms: 0 + 9 = 9 z = 9 Simplifying z = 9

Subproblem 2

Set the factor '(4 + -5z)' equal to zero and attempt to solve: Simplifying 4 + -5z = 0 Solving 4 + -5z = 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 + -5z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5z = 0 + -4 -5z = 0 + -4 Combine like terms: 0 + -4 = -4 -5z = -4 Divide each side by '-5'. z = 0.8 Simplifying z = 0.8

Solution

z = {9, 0.8}

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