=2z^2-7z+3

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

Simplifying
0 = 2z2 + -7z + 3

Reorder the terms:
0 = 3 + -7z + 2z2

Solving
0 = 3 + -7z + 2z2

Solving for variable 'z'.

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

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

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

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

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

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

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

Simplifying
-3 + z = 0

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

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

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

Simplifying
z = 3
Subproblem 2
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
Solution
z = {3, 0.5}