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

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


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

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

Multiply (4 + -1z) * (-7 + 4z)
(4(-7 + 4z) + -1z * (-7 + 4z)) = 0
((-7 * 4 + 4z * 4) + -1z * (-7 + 4z)) = 0
((-28 + 16z) + -1z * (-7 + 4z)) = 0
(-28 + 16z + (-7 * -1z + 4z * -1z)) = 0
(-28 + 16z + (7z + -4z2)) = 0

Combine like terms: 16z + 7z = 23z
(-28 + 23z + -4z2) = 0

Solving
-28 + 23z + -4z2 = 0

Solving for variable 'z'.

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


Subproblem 1
Set the factor '(-4 + z)' equal to zero and attempt to solve:

Simplifying
-4 + z = 0

Solving
-4 + z = 0

Move all terms containing z to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + z = 0 + 4
z = 0 + 4

Combine like terms: 0 + 4 = 4
z = 4

Simplifying
z = 4

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 = {4, 1.75}

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