2z^2+z-2=3z-7

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

Simplifying
2z2 + z + -2 = 3z + -7

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

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

Solving
-2 + z + 2z2 = -7 + 3z

Solving for variable 'z'.

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

Combine like terms: -2 + 7 = 5
5 + z + -3z + 2z2 = -7 + 3z + 7 + -3z

Combine like terms: z + -3z = -2z
5 + -2z + 2z2 = -7 + 3z + 7 + -3z

Reorder the terms:
5 + -2z + 2z2 = -7 + 7 + 3z + -3z

Combine like terms: -7 + 7 = 0
5 + -2z + 2z2 = 0 + 3z + -3z
5 + -2z + 2z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
5 + -2z + 2z2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
2.5 + -1z + z2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -1z + -2.5 + z2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -1z + z2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -1z + z2 = 0 + -2.5
-1z + z2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-1z + z2 = -2.5

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -2.5 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -2.5 + 0.25

Combine like terms: -2.5 + 0.25 = -2.25
0.25 + -1z + z2 = -2.25

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -2.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.