9z^2+14z=8z-1

Solution for 9z^2+14z=8z-1 equation:

Simplifying
9z2 + 14z = 8z + -1

Reorder the terms:
14z + 9z2 = 8z + -1

Reorder the terms:
14z + 9z2 = -1 + 8z

Solving
14z + 9z2 = -1 + 8z

Solving for variable 'z'.

Reorder the terms:
1 + 14z + -8z + 9z2 = -1 + 8z + 1 + -8z

Combine like terms: 14z + -8z = 6z
1 + 6z + 9z2 = -1 + 8z + 1 + -8z

Reorder the terms:
1 + 6z + 9z2 = -1 + 1 + 8z + -8z

Combine like terms: -1 + 1 = 0
1 + 6z + 9z2 = 0 + 8z + -8z
1 + 6z + 9z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
1 + 6z + 9z2 = 0

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

Subproblem 1
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 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 + 3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3z = 0 + -1
3z = 0 + -1

Combine like terms: 0 + -1 = -1
3z = -1

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 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 + 3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3z = 0 + -1
3z = 0 + -1

Combine like terms: 0 + -1 = -1
3z = -1

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {-0.3333333333, -0.3333333333}