a+2a+(2a^2)=90

Solution for a+2a+(2a^2)=90 equation:

Simplifying
a + 2a + (2a2) = 90

Combine like terms: a + 2a = 3a
3a + (2a2) = 90

Solving
3a + (2a2) = 90

Solving for variable 'a'.

Reorder the terms:
-90 + 3a + (2a2) = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 3a + (2a2) = 0

Factor a trinomial.
(-15 + -2a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-15 + -2a)' equal to zero and attempt to solve:

Simplifying
-15 + -2a = 0

Solving
-15 + -2a = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2a = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2a = 0 + 15
-2a = 0 + 15

Combine like terms: 0 + 15 = 15
-2a = 15

Divide each side by '-2'.
a = -7.5

Simplifying
a = -7.5
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 = {-7.5, 6}