(x+5a)(x-4a)=

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

Simplifying
(x + 5a)(x + -4a) = 0

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

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

Multiply (5a + x) * (-4a + x)
(5a * (-4a + x) + x(-4a + x)) = 0
((-4a * 5a + x * 5a) + x(-4a + x)) = 0

Reorder the terms:
((5ax + -20a2) + x(-4a + x)) = 0
((5ax + -20a2) + x(-4a + x)) = 0
(5ax + -20a2 + (-4a * x + x * x)) = 0
(5ax + -20a2 + (-4ax + x2)) = 0

Reorder the terms:
(5ax + -4ax + -20a2 + x2) = 0

Combine like terms: 5ax + -4ax = 1ax
(1ax + -20a2 + x2) = 0

Solving
1ax + -20a2 + x2 = 0

Solving for variable 'a'.

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

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

Simplifying
-5a + -1x = 0

Solving
-5a + -1x = 0

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

Add 'x' to each side of the equation.
-5a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-5a + 0 = 0 + x
-5a = 0 + x
Remove the zero:
-5a = x

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

Simplifying
a = -0.2x
Subproblem 2
Set the factor '(4a + -1x)' equal to zero and attempt to solve:

Simplifying
4a + -1x = 0

Solving
4a + -1x = 0

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

Add 'x' to each side of the equation.
4a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
4a + 0 = 0 + x
4a = 0 + x
Remove the zero:
4a = x

Divide each side by '4'.
a = 0.25x

Simplifying
a = 0.25x
Solution
a = {-0.2x, 0.25x}