2z^2=7z-6

Solution for 2z^2=7z-6 equation:

Simplifying
2z2 = 7z + -6

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

Solving
2z2 = -6 + 7z

Solving for variable 'z'.

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

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

Combine like terms: -6 + 6 = 0
6 + -7z + 2z2 = 0 + 7z + -7z
6 + -7z + 2z2 = 7z + -7z

Combine like terms: 7z + -7z = 0
6 + -7z + 2z2 = 0

Factor a trinomial.
(3 + -2z)(2 + -1z) = 0

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

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {1.5, 2}