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

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


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

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

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

Combine like terms: -2z + 20z = 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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