7z^2+31z+2=6z^2+35z-1

Solution for 7z^2+31z+2=6z^2+35z-1 equation:

Simplifying
7z2 + 31z + 2 = 6z2 + 35z + -1

Reorder the terms:
2 + 31z + 7z2 = 6z2 + 35z + -1

Reorder the terms:
2 + 31z + 7z2 = -1 + 35z + 6z2

Solving
2 + 31z + 7z2 = -1 + 35z + 6z2

Solving for variable 'z'.

Reorder the terms:
2 + 1 + 31z + -35z + 7z2 + -6z2 = -1 + 35z + 6z2 + 1 + -35z + -6z2

Combine like terms: 2 + 1 = 3
3 + 31z + -35z + 7z2 + -6z2 = -1 + 35z + 6z2 + 1 + -35z + -6z2

Combine like terms: 31z + -35z = -4z
3 + -4z + 7z2 + -6z2 = -1 + 35z + 6z2 + 1 + -35z + -6z2

Combine like terms: 7z2 + -6z2 = 1z2
3 + -4z + 1z2 = -1 + 35z + 6z2 + 1 + -35z + -6z2

Reorder the terms:
3 + -4z + 1z2 = -1 + 1 + 35z + -35z + 6z2 + -6z2

Combine like terms: -1 + 1 = 0
3 + -4z + 1z2 = 0 + 35z + -35z + 6z2 + -6z2
3 + -4z + 1z2 = 35z + -35z + 6z2 + -6z2

Combine like terms: 35z + -35z = 0
3 + -4z + 1z2 = 0 + 6z2 + -6z2
3 + -4z + 1z2 = 6z2 + -6z2

Combine like terms: 6z2 + -6z2 = 0
3 + -4z + 1z2 = 0

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

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 '(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 = {1, 3}