x(4m+x)=96m^2

Solution for x(4m+x)=96m^2 equation:

Simplifying
x(4m + x) = 96m2
(4m * x + x * x) = 96m2
(4mx + x2) = 96m2

Solving
4mx + x2 = 96m2

Solving for variable 'm'.

Reorder the terms:
4mx + -96m2 + x2 = 96m2 + -96m2

Combine like terms: 96m2 + -96m2 = 0
4mx + -96m2 + x2 = 0

Factor a trinomial.
(-12m + -1x)(8m + -1x) = 0

Subproblem 1
Set the factor '(-12m + -1x)' equal to zero and attempt to solve:

Simplifying
-12m + -1x = 0

Solving
-12m + -1x = 0

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

Add 'x' to each side of the equation.
-12m + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-12m + 0 = 0 + x
-12m = 0 + x
Remove the zero:
-12m = x

Divide each side by '-12'.
m = -0.08333333333x

Simplifying
m = -0.08333333333x
Subproblem 2
Set the factor '(8m + -1x)' equal to zero and attempt to solve:

Simplifying
8m + -1x = 0

Solving
8m + -1x = 0

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

Add 'x' to each side of the equation.
8m + -1x + x = 0 + x

Combine like terms: -1x + x = 0
8m + 0 = 0 + x
8m = 0 + x
Remove the zero:
8m = x

Divide each side by '8'.
m = 0.125x

Simplifying
m = 0.125x
Solution
m = {-0.08333333333x, 0.125x}