(3a^2-5a+3)-(a^2+a-2)=

Solution for (3a^2-5a+3)-(a^2+a-2)= equation:

Simplifying
(3a2 + -5a + 3) + -1(a2 + a + -2) = 0

Reorder the terms:
(3 + -5a + 3a2) + -1(a2 + a + -2) = 0

Remove parenthesis around (3 + -5a + 3a2)
3 + -5a + 3a2 + -1(a2 + a + -2) = 0

Reorder the terms:
3 + -5a + 3a2 + -1(-2 + a + a2) = 0
3 + -5a + 3a2 + (-2 * -1 + a * -1 + a2 * -1) = 0
3 + -5a + 3a2 + (2 + -1a + -1a2) = 0

Reorder the terms:
3 + 2 + -5a + -1a + 3a2 + -1a2 = 0

Combine like terms: 3 + 2 = 5
5 + -5a + -1a + 3a2 + -1a2 = 0

Combine like terms: -5a + -1a = -6a
5 + -6a + 3a2 + -1a2 = 0

Combine like terms: 3a2 + -1a2 = 2a2
5 + -6a + 2a2 = 0

Solving
5 + -6a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
2.5 + -3a + a2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3a + -2.5 + a2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3a + a2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3a + a2 = 0 + -2.5
-3a + a2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3a + a2 = -2.5

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = -2.5 + 2.25

Reorder the terms:
2.25 + -3a + a2 = -2.5 + 2.25

Combine like terms: -2.5 + 2.25 = -0.25
2.25 + -3a + a2 = -0.25

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.