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

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Solution for (7-z)(4z+1)=0 equation:


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

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

Multiply (7 + -1z) * (1 + 4z)
(7(1 + 4z) + -1z * (1 + 4z)) = 0
((1 * 7 + 4z * 7) + -1z * (1 + 4z)) = 0
((7 + 28z) + -1z * (1 + 4z)) = 0
(7 + 28z + (1 * -1z + 4z * -1z)) = 0
(7 + 28z + (-1z + -4z2)) = 0

Combine like terms: 28z + -1z = 27z
(7 + 27z + -4z2) = 0

Solving
7 + 27z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + -1z)(1 + 4z) = 0

Subproblem 1

Set the factor '(7 + -1z)' equal to zero and attempt to solve: Simplifying 7 + -1z = 0 Solving 7 + -1z = 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 + -1z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1z = 0 + -7 -1z = 0 + -7 Combine like terms: 0 + -7 = -7 -1z = -7 Divide each side by '-1'. z = 7 Simplifying z = 7

Subproblem 2

Set the factor '(1 + 4z)' equal to zero and attempt to solve: Simplifying 1 + 4z = 0 Solving 1 + 4z = 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 + 4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4z = 0 + -1 4z = 0 + -1 Combine like terms: 0 + -1 = -1 4z = -1 Divide each side by '4'. z = -0.25 Simplifying z = -0.25

Solution

z = {7, -0.25}

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