10a^2-20a-78=2

Solution for 10a^2-20a-78=2 equation:

Simplifying
10a2 + -20a + -78 = 2

Reorder the terms:
-78 + -20a + 10a2 = 2

Solving
-78 + -20a + 10a2 = 2

Solving for variable 'a'.

Reorder the terms:
-78 + -2 + -20a + 10a2 = 2 + -2

Combine like terms: -78 + -2 = -80
-80 + -20a + 10a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-80 + -20a + 10a2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + -2a + a2) = 0

Factor a trinomial.
10((-2 + -1a)(4 + -1a)) = 0

Ignore the factor 10.
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 '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2, 4}