2(z-5)(-z+4)=0

Solution for 2(z-5)(-z+4)=0 equation:

Simplifying
2(z + -5)(-1z + 4) = 0

Reorder the terms:
2(-5 + z)(-1z + 4) = 0

Reorder the terms:
2(-5 + z)(4 + -1z) = 0

Multiply (-5 + z) * (4 + -1z)
2(-5(4 + -1z) + z(4 + -1z)) = 0
2((4 * -5 + -1z * -5) + z(4 + -1z)) = 0
2((-20 + 5z) + z(4 + -1z)) = 0
2(-20 + 5z + (4 * z + -1z * z)) = 0
2(-20 + 5z + (4z + -1z2)) = 0

Combine like terms: 5z + 4z = 9z
2(-20 + 9z + -1z2) = 0
(-20 * 2 + 9z * 2 + -1z2 * 2) = 0
(-40 + 18z + -2z2) = 0

Solving
-40 + 18z + -2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 9z + -1z2) = 0

Factor a trinomial.
2((-5 + z)(4 + -1z)) = 0

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

Simplifying
-5 + z = 0

Solving
-5 + z = 0

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

Add '5' to each side of the equation.
-5 + 5 + z = 0 + 5

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

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

Simplifying
z = 5
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {5, 4}