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

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

Simplifying
(4a + x)(a + -1x) = 0

Multiply (4a + x) * (a + -1x)
(4a * (a + -1x) + x(a + -1x)) = 0
((a * 4a + -1x * 4a) + x(a + -1x)) = 0

Reorder the terms:
((-4ax + 4a2) + x(a + -1x)) = 0
((-4ax + 4a2) + x(a + -1x)) = 0
(-4ax + 4a2 + (a * x + -1x * x)) = 0
(-4ax + 4a2 + (ax + -1x2)) = 0

Reorder the terms:
(-4ax + ax + 4a2 + -1x2) = 0

Combine like terms: -4ax + ax = -3ax
(-3ax + 4a2 + -1x2) = 0

Solving
-3ax + 4a2 + -1x2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

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

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

Simplifying
4a + x = 0

Solving
4a + x = 0

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

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

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

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

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