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

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


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

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

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

Combine like terms: 36z + 5z = 41z
(45 + 41z + 4z2) = 0

Solving
45 + 41z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + z)(5 + 4z) = 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 '(5 + 4z)' equal to zero and attempt to solve: Simplifying 5 + 4z = 0 Solving 5 + 4z = 0 Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4z = 0 + -5 4z = 0 + -5 Combine like terms: 0 + -5 = -5 4z = -5 Divide each side by '4'. z = -1.25 Simplifying z = -1.25

Solution

z = {-9, -1.25}

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