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

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


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

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

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

Combine like terms: 28z + -2z = 26z
(-14 + 26z + 4z2) = 0

Solving
-14 + 26z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 13z + 2z2) = 0

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

Ignore the factor 2.

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 + -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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