a(1+2a)-a(4a-5)=

Solution for a(1+2a)-a(4a-5)= equation:

Simplifying
a(1 + 2a) + -1a(4a + -5) = 0
(1 * a + 2a * a) + -1a(4a + -5) = 0
(1a + 2a2) + -1a(4a + -5) = 0

Reorder the terms:
1a + 2a2 + -1a(-5 + 4a) = 0
1a + 2a2 + (-5 * -1a + 4a * -1a) = 0
1a + 2a2 + (5a + -4a2) = 0

Reorder the terms:
1a + 5a + 2a2 + -4a2 = 0

Combine like terms: 1a + 5a = 6a
6a + 2a2 + -4a2 = 0

Combine like terms: 2a2 + -4a2 = -2a2
6a + -2a2 = 0

Solving
6a + -2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(3 + -1a) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {0, 3}