(4z-2)(7-z)=0

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Solution for (4z-2)(7-z)=0 equation: 


Simplifying
(4z + -2)(7 + -1z) = 0

Reorder the terms:
(-2 + 4z)(7 + -1z) = 0

Multiply (-2 + 4z) * (7 + -1z)
(-2(7 + -1z) + 4z * (7 + -1z)) = 0
((7 * -2 + -1z * -2) + 4z * (7 + -1z)) = 0
((-14 + 2z) + 4z * (7 + -1z)) = 0
(-14 + 2z + (7 * 4z + -1z * 4z)) = 0
(-14 + 2z + (28z + -4z2)) = 0

Combine like terms: 2z + 28z = 30z
(-14 + 30z + -4z2) = 0

Solving
-14 + 30z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 15z + -2z2) = 0

Factor a trinomial.
2((-7 + z)(1 + -2z)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve:

Simplifying
-7 + z = 0

Solving
-7 + z = 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 + z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + z = 0 + 7
z = 0 + 7

Combine like terms: 0 + 7 = 7
z = 7

Simplifying
z = 7

Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {7, 0.5}

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