(5z-1)(8z-5)=0

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Solution for (5z-1)(8z-5)=0 equation:


Simplifying
(5z + -1)(8z + -5) = 0

Reorder the terms:
(-1 + 5z)(8z + -5) = 0

Reorder the terms:
(-1 + 5z)(-5 + 8z) = 0

Multiply (-1 + 5z) * (-5 + 8z)
(-1(-5 + 8z) + 5z * (-5 + 8z)) = 0
((-5 * -1 + 8z * -1) + 5z * (-5 + 8z)) = 0
((5 + -8z) + 5z * (-5 + 8z)) = 0
(5 + -8z + (-5 * 5z + 8z * 5z)) = 0
(5 + -8z + (-25z + 40z2)) = 0

Combine like terms: -8z + -25z = -33z
(5 + -33z + 40z2) = 0

Solving
5 + -33z + 40z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -5z)(5 + -8z) = 0

Subproblem 1

Set the factor '(1 + -5z)' equal to zero and attempt to solve: Simplifying 1 + -5z = 0 Solving 1 + -5z = 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 + -5z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5z = 0 + -1 -5z = 0 + -1 Combine like terms: 0 + -1 = -1 -5z = -1 Divide each side by '-5'. z = 0.2 Simplifying z = 0.2

Subproblem 2

Set the factor '(5 + -8z)' equal to zero and attempt to solve: Simplifying 5 + -8z = 0 Solving 5 + -8z = 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 + -8z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8z = 0 + -5 -8z = 0 + -5 Combine like terms: 0 + -5 = -5 -8z = -5 Divide each side by '-8'. z = 0.625 Simplifying z = 0.625

Solution

z = {0.2, 0.625}

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