(5a^2-7a+1)-(2a^2+3a-6)=0

Solution for (5a^2-7a+1)-(2a^2+3a-6)=0 equation:

Simplifying
(5a2 + -7a + 1) + -1(2a2 + 3a + -6) = 0

Reorder the terms:
(1 + -7a + 5a2) + -1(2a2 + 3a + -6) = 0

Remove parenthesis around (1 + -7a + 5a2)
1 + -7a + 5a2 + -1(2a2 + 3a + -6) = 0

Reorder the terms:
1 + -7a + 5a2 + -1(-6 + 3a + 2a2) = 0
1 + -7a + 5a2 + (-6 * -1 + 3a * -1 + 2a2 * -1) = 0
1 + -7a + 5a2 + (6 + -3a + -2a2) = 0

Reorder the terms:
1 + 6 + -7a + -3a + 5a2 + -2a2 = 0

Combine like terms: 1 + 6 = 7
7 + -7a + -3a + 5a2 + -2a2 = 0

Combine like terms: -7a + -3a = -10a
7 + -10a + 5a2 + -2a2 = 0

Combine like terms: 5a2 + -2a2 = 3a2
7 + -10a + 3a2 = 0

Solving
7 + -10a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -1a)(7 + -3a) = 0

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Subproblem 2
Set the factor '(7 + -3a)' equal to zero and attempt to solve:

Simplifying
7 + -3a = 0

Solving
7 + -3a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3a = 0 + -7
-3a = 0 + -7

Combine like terms: 0 + -7 = -7
-3a = -7

Divide each side by '-3'.
a = 2.333333333

Simplifying
a = 2.333333333
Solution
a = {1, 2.333333333}