x^2+ax=20a^2

Solution for x^2+ax=20a^2 equation:

Simplifying
x2 + ax = 20a2

Reorder the terms:
ax + x2 = 20a2

Solving
ax + x2 = 20a2

Solving for variable 'a'.

Reorder the terms:
ax + -20a2 + x2 = 20a2 + -20a2

Combine like terms: 20a2 + -20a2 = 0
ax + -20a2 + x2 = 0

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}