(5z-7)(2-z)=0

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Solution for (5z-7)(2-z)=0 equation:


Simplifying
(5z + -7)(2 + -1z) = 0

Reorder the terms:
(-7 + 5z)(2 + -1z) = 0

Multiply (-7 + 5z) * (2 + -1z)
(-7(2 + -1z) + 5z * (2 + -1z)) = 0
((2 * -7 + -1z * -7) + 5z * (2 + -1z)) = 0
((-14 + 7z) + 5z * (2 + -1z)) = 0
(-14 + 7z + (2 * 5z + -1z * 5z)) = 0
(-14 + 7z + (10z + -5z2)) = 0

Combine like terms: 7z + 10z = 17z
(-14 + 17z + -5z2) = 0

Solving
-14 + 17z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + z)(7 + -5z) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -5z)' equal to zero and attempt to solve: Simplifying 7 + -5z = 0 Solving 7 + -5z = 0 Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5z = 0 + -7 -5z = 0 + -7 Combine like terms: 0 + -7 = -7 -5z = -7 Divide each side by '-5'. z = 1.4 Simplifying z = 1.4

Solution

z = {2, 1.4}

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