(5+z)(4z-2)=0

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Solution for (5+z)(4z-2)=0 equation:


Simplifying
(5 + z)(4z + -2) = 0

Reorder the terms:
(5 + z)(-2 + 4z) = 0

Multiply (5 + z) * (-2 + 4z)
(5(-2 + 4z) + z(-2 + 4z)) = 0
((-2 * 5 + 4z * 5) + z(-2 + 4z)) = 0
((-10 + 20z) + z(-2 + 4z)) = 0
(-10 + 20z + (-2 * z + 4z * z)) = 0
(-10 + 20z + (-2z + 4z2)) = 0

Combine like terms: 20z + -2z = 18z
(-10 + 18z + 4z2) = 0

Solving
-10 + 18z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9z + 2z2) = 0

Factor a trinomial.
2((-5 + -1z)(1 + -2z)) = 0

Ignore the factor 2.

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 '(1 + -2z)' equal to zero and attempt to solve: Simplifying 1 + -2z = 0 Solving 1 + -2z = 0 Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2z = 0 + -1 -2z = 0 + -1 Combine like terms: 0 + -1 = -1 -2z = -1 Divide each side by '-2'. z = 0.5 Simplifying z = 0.5

Solution

z = {-5, 0.5}

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