a(1+2a)=10

Solution for a(1+2a)=10 equation:

Simplifying
a(1 + 2a) = 10
(1 * a + 2a * a) = 10
(1a + 2a2) = 10

Solving
1a + 2a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + 1a + 2a2 = 10 + -10

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

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-2.5, 2}