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

Solution for (5z-7)(1+z)=0 equation:

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

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

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

Combine like terms: -7z + 5z = -2z
(-7 + -2z + 5z2) = 0

Solving
-7 + -2z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(7 + -5z) = 0

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

Simplifying
-1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(7 + -5z)' equal to zero and attempt to solve:

Simplifying
7 + -5z = 0

Solving
7 + -5z = 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 + -5z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5z = 0 + -7
-5z = 0 + -7

Combine like terms: 0 + -7 = -7
-5z = -7

Divide each side by '-5'.
z = 1.4

Simplifying
z = 1.4
Solution
z = {-1, 1.4}