-2a(1+2a)-7a(5+4a)=

Solution for -2a(1+2a)-7a(5+4a)= equation:

Simplifying
-2a(1 + 2a) + -7a(5 + 4a) = 0
(1 * -2a + 2a * -2a) + -7a(5 + 4a) = 0
(-2a + -4a2) + -7a(5 + 4a) = 0
-2a + -4a2 + (5 * -7a + 4a * -7a) = 0
-2a + -4a2 + (-35a + -28a2) = 0

Reorder the terms:
-2a + -35a + -4a2 + -28a2 = 0

Combine like terms: -2a + -35a = -37a
-37a + -4a2 + -28a2 = 0

Combine like terms: -4a2 + -28a2 = -32a2
-37a + -32a2 = 0

Solving
-37a + -32a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(37 + 32a) = 0

Ignore the factor -1.
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 '(37 + 32a)' equal to zero and attempt to solve:

Simplifying
37 + 32a = 0

Solving
37 + 32a = 0

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

Add '-37' to each side of the equation.
37 + -37 + 32a = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 32a = 0 + -37
32a = 0 + -37

Combine like terms: 0 + -37 = -37
32a = -37

Divide each side by '32'.
a = -1.15625

Simplifying
a = -1.15625
Solution
a = {0, -1.15625}