56z^2=22z-2

Solution for 56z^2=22z-2 equation:

Simplifying
56z2 = 22z + -2

Reorder the terms:
56z2 = -2 + 22z

Solving
56z2 = -2 + 22z

Solving for variable 'z'.

Reorder the terms:
2 + -22z + 56z2 = -2 + 22z + 2 + -22z

Reorder the terms:
2 + -22z + 56z2 = -2 + 2 + 22z + -22z

Combine like terms: -2 + 2 = 0
2 + -22z + 56z2 = 0 + 22z + -22z
2 + -22z + 56z2 = 22z + -22z

Combine like terms: 22z + -22z = 0
2 + -22z + 56z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -11z + 28z2) = 0

Factor a trinomial.
2((1 + -7z)(1 + -4z)) = 0

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

Simplifying
1 + -7z = 0

Solving
1 + -7z = 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 + -7z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7z = 0 + -1
-7z = 0 + -1

Combine like terms: 0 + -1 = -1
-7z = -1

Divide each side by '-7'.
z = 0.1428571429

Simplifying
z = 0.1428571429
Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

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

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

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

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {0.1428571429, 0.25}