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

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

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

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

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

Multiply (-2 + 4a) * (1 + 5a)
(-2(1 + 5a) + 4a * (1 + 5a)) = 0
((1 * -2 + 5a * -2) + 4a * (1 + 5a)) = 0
((-2 + -10a) + 4a * (1 + 5a)) = 0
(-2 + -10a + (1 * 4a + 5a * 4a)) = 0
(-2 + -10a + (4a + 20a2)) = 0

Combine like terms: -10a + 4a = -6a
(-2 + -6a + 20a2) = 0

Solving
-2 + -6a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3a + 10a2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5a)' equal to zero and attempt to solve:

Simplifying
-1 + -5a = 0

Solving
-1 + -5a = 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 + -5a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5a = 0 + 1
-5a = 0 + 1

Combine like terms: 0 + 1 = 1
-5a = 1

Divide each side by '-5'.
a = -0.2

Simplifying
a = -0.2
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 = {-0.2, 0.5}