(2z-7)(-z+3)=

Solution for (2z-7)(-z+3)= equation:

Simplifying
(2z + -7)(-1z + 3) = 0

Reorder the terms:
(-7 + 2z)(-1z + 3) = 0

Reorder the terms:
(-7 + 2z)(3 + -1z) = 0

Multiply (-7 + 2z) * (3 + -1z)
(-7(3 + -1z) + 2z * (3 + -1z)) = 0
((3 * -7 + -1z * -7) + 2z * (3 + -1z)) = 0
((-21 + 7z) + 2z * (3 + -1z)) = 0
(-21 + 7z + (3 * 2z + -1z * 2z)) = 0
(-21 + 7z + (6z + -2z2)) = 0

Combine like terms: 7z + 6z = 13z
(-21 + 13z + -2z2) = 0

Solving
-21 + 13z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + 2z)(3 + -1z) = 0

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

Simplifying
-7 + 2z = 0

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

Combine like terms: -7 + 7 = 0
0 + 2z = 0 + 7
2z = 0 + 7

Combine like terms: 0 + 7 = 7
2z = 7

Divide each side by '2'.
z = 3.5

Simplifying
z = 3.5
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {3.5, 3}