2a+2a^2=84

Solution for 2a+2a^2=84 equation:

Simplifying
2a + 2a2 = 84

Solving
2a + 2a2 = 84

Solving for variable 'a'.

Reorder the terms:
-84 + 2a + 2a2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 2a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + a + a2) = 0

Factor a trinomial.
2((-7 + -1a)(6 + -1a)) = 0

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

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 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 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-7, 6}