(2a-1)(a+3a+5)=

Solution for (2a-1)(a+3a+5)= equation:

Simplifying
(2a + -1)(a + 3a + 5) = 0

Reorder the terms:
(-1 + 2a)(a + 3a + 5) = 0

Reorder the terms:
(-1 + 2a)(5 + a + 3a) = 0

Combine like terms: a + 3a = 4a
(-1 + 2a)(5 + 4a) = 0

Multiply (-1 + 2a) * (5 + 4a)
(-1(5 + 4a) + 2a * (5 + 4a)) = 0
((5 * -1 + 4a * -1) + 2a * (5 + 4a)) = 0
((-5 + -4a) + 2a * (5 + 4a)) = 0
(-5 + -4a + (5 * 2a + 4a * 2a)) = 0
(-5 + -4a + (10a + 8a2)) = 0

Combine like terms: -4a + 10a = 6a
(-5 + 6a + 8a2) = 0

Solving
-5 + 6a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -4a)(1 + -2a) = 0

Subproblem 1
Set the factor '(-5 + -4a)' equal to zero and attempt to solve:

Simplifying
-5 + -4a = 0

Solving
-5 + -4a = 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 + -4a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4a = 0 + 5
-4a = 0 + 5

Combine like terms: 0 + 5 = 5
-4a = 5

Divide each side by '-4'.
a = -1.25

Simplifying
a = -1.25
Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

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

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

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-1.25, 0.5}