(4z+7)(5-z)=0

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Solution for (4z+7)(5-z)=0 equation:


Simplifying
(4z + 7)(5 + -1z) = 0

Reorder the terms:
(7 + 4z)(5 + -1z) = 0

Multiply (7 + 4z) * (5 + -1z)
(7(5 + -1z) + 4z * (5 + -1z)) = 0
((5 * 7 + -1z * 7) + 4z * (5 + -1z)) = 0
((35 + -7z) + 4z * (5 + -1z)) = 0
(35 + -7z + (5 * 4z + -1z * 4z)) = 0
(35 + -7z + (20z + -4z2)) = 0

Combine like terms: -7z + 20z = 13z
(35 + 13z + -4z2) = 0

Solving
35 + 13z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + -1z)(7 + 4z) = 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 '(7 + 4z)' equal to zero and attempt to solve: Simplifying 7 + 4z = 0 Solving 7 + 4z = 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 + 4z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4z = 0 + -7 4z = 0 + -7 Combine like terms: 0 + -7 = -7 4z = -7 Divide each side by '4'. z = -1.75 Simplifying z = -1.75

Solution

z = {5, -1.75}

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