2z^2=7z-3

Solution for 2z^2=7z-3 equation:

Simplifying
2z2 = 7z + -3

Reorder the terms:
2z2 = -3 + 7z

Solving
2z2 = -3 + 7z

Solving for variable 'z'.

Reorder the terms:
3 + -7z + 2z2 = -3 + 7z + 3 + -7z

Reorder the terms:
3 + -7z + 2z2 = -3 + 3 + 7z + -7z

Combine like terms: -3 + 3 = 0
3 + -7z + 2z2 = 0 + 7z + -7z
3 + -7z + 2z2 = 7z + -7z

Combine like terms: 7z + -7z = 0
3 + -7z + 2z2 = 0

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

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
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 = {0.5, 3}