2a^2-a-7=3

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

Simplifying
2a2 + -1a + -7 = 3

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

Solving
-7 + -1a + 2a2 = 3

Solving for variable 'a'.

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

Combine like terms: -7 + -3 = -10
-10 + -1a + 2a2 = 3 + -3

Combine like terms: 3 + -3 = 0
-10 + -1a + 2a2 = 0

Factor a trinomial.
(-2 + -1a)(5 + -2a) = 0

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

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1a = 0 + 2

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(5 + -2a)' equal to zero and attempt to solve:

Simplifying
5 + -2a = 0

Solving
5 + -2a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2a = 0 + -5
-2a = 0 + -5

Combine like terms: 0 + -5 = -5
-2a = -5

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
Solution
a = {-2, 2.5}