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

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


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

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

Multiply (5 + z) * (-4 + 5z)
(5(-4 + 5z) + z(-4 + 5z)) = 0
((-4 * 5 + 5z * 5) + z(-4 + 5z)) = 0
((-20 + 25z) + z(-4 + 5z)) = 0
(-20 + 25z + (-4 * z + 5z * z)) = 0
(-20 + 25z + (-4z + 5z2)) = 0

Combine like terms: 25z + -4z = 21z
(-20 + 21z + 5z2) = 0

Solving
-20 + 21z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(4 + -5z) = 0

Subproblem 1

Set the factor '(-5 + -1z)' equal to zero and attempt to solve: Simplifying -5 + -1z = 0 Solving -5 + -1z = 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 + -1z = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1z = 0 + 5 -1z = 0 + 5 Combine like terms: 0 + 5 = 5 -1z = 5 Divide each side by '-1'. z = -5 Simplifying z = -5

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 = {-5, 0.8}

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