10z^2=40z+50

Solution for 10z^2=40z+50 equation:

Simplifying
10z2 = 40z + 50

Reorder the terms:
10z2 = 50 + 40z

Solving
10z2 = 50 + 40z

Solving for variable 'z'.

Reorder the terms:
-50 + -40z + 10z2 = 50 + 40z + -50 + -40z

Reorder the terms:
-50 + -40z + 10z2 = 50 + -50 + 40z + -40z

Combine like terms: 50 + -50 = 0
-50 + -40z + 10z2 = 0 + 40z + -40z
-50 + -40z + 10z2 = 40z + -40z

Combine like terms: 40z + -40z = 0
-50 + -40z + 10z2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + -4z + z2) = 0

Factor a trinomial.
10((-1 + -1z)(5 + -1z)) = 0

Ignore the factor 10.
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 '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {-1, 5}