14z^2-49z+35=0

Solution for 14z^2-49z+35=0 equation:

Simplifying
14z2 + -49z + 35 = 0

Reorder the terms:
35 + -49z + 14z2 = 0

Solving
35 + -49z + 14z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7'.
7(5 + -7z + 2z2) = 0

Factor a trinomial.
7((1 + -1z)(5 + -2z)) = 0

Ignore the factor 7.
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 + -2z)' equal to zero and attempt to solve:

Simplifying
5 + -2z = 0

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

Combine like terms: 5 + -5 = 0
0 + -2z = 0 + -5
-2z = 0 + -5

Combine like terms: 0 + -5 = -5
-2z = -5

Divide each side by '-2'.
z = 2.5

Simplifying
z = 2.5
Solution
z = {1, 2.5}