(x-a)(a+5)-4a=4(2x-3a)-3(x-2a)

Solution for (x-a)(a+5)-4a=4(2x-3a)-3(x-2a) equation:

Simplifying
(x + -1a)(a + 5) + -4a = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
(-1a + x)(a + 5) + -4a = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
(-1a + x)(5 + a) + -4a = 4(2x + -3a) + -3(x + -2a)

Multiply (-1a + x) * (5 + a)
(-1a * (5 + a) + x(5 + a)) + -4a = 4(2x + -3a) + -3(x + -2a)
((5 * -1a + a * -1a) + x(5 + a)) + -4a = 4(2x + -3a) + -3(x + -2a)
((-5a + -1a2) + x(5 + a)) + -4a = 4(2x + -3a) + -3(x + -2a)
(-5a + -1a2 + (5 * x + a * x)) + -4a = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
(-5a + -1a2 + (ax + 5x)) + -4a = 4(2x + -3a) + -3(x + -2a)
(-5a + -1a2 + (ax + 5x)) + -4a = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
(-5a + ax + -1a2 + 5x) + -4a = 4(2x + -3a) + -3(x + -2a)
(-5a + ax + -1a2 + 5x) + -4a = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
-5a + -4a + ax + -1a2 + 5x = 4(2x + -3a) + -3(x + -2a)

Combine like terms: -5a + -4a = -9a
-9a + ax + -1a2 + 5x = 4(2x + -3a) + -3(x + -2a)

Reorder the terms:
-9a + ax + -1a2 + 5x = 4(-3a + 2x) + -3(x + -2a)
-9a + ax + -1a2 + 5x = (-3a * 4 + 2x * 4) + -3(x + -2a)
-9a + ax + -1a2 + 5x = (-12a + 8x) + -3(x + -2a)

Reorder the terms:
-9a + ax + -1a2 + 5x = -12a + 8x + -3(-2a + x)
-9a + ax + -1a2 + 5x = -12a + 8x + (-2a * -3 + x * -3)
-9a + ax + -1a2 + 5x = -12a + 8x + (6a + -3x)

Reorder the terms:
-9a + ax + -1a2 + 5x = -12a + 6a + 8x + -3x

Combine like terms: -12a + 6a = -6a
-9a + ax + -1a2 + 5x = -6a + 8x + -3x

Combine like terms: 8x + -3x = 5x
-9a + ax + -1a2 + 5x = -6a + 5x

Add '-5x' to each side of the equation.
-9a + ax + -1a2 + 5x + -5x = -6a + 5x + -5x

Combine like terms: 5x + -5x = 0
-9a + ax + -1a2 + 0 = -6a + 5x + -5x
-9a + ax + -1a2 = -6a + 5x + -5x

Combine like terms: 5x + -5x = 0
-9a + ax + -1a2 = -6a + 0
-9a + ax + -1a2 = -6a

Solving
-9a + ax + -1a2 = -6a

Solving for variable 'a'.

Reorder the terms:
-9a + 6a + ax + -1a2 = -6a + 6a

Combine like terms: -9a + 6a = -3a
-3a + ax + -1a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
-3a + ax + -1a2 = 0

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

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-3 + x + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + x + -1a = 0

Reorder the terms:
-3 + -1a + x = 0

Solving
-3 + -1a + x = 0

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

Add '3' to each side of the equation.
-3 + -1a + 3 + x = 0 + 3

Reorder the terms:
-3 + 3 + -1a + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a + x = 0 + 3
-1a + x = 0 + 3

Combine like terms: 0 + 3 = 3
-1a + x = 3

Add '-1x' to each side of the equation.
-1a + x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
-1a + 0 = 3 + -1x
-1a = 3 + -1x

Divide each side by '-1'.
a = -3 + x

Simplifying
a = -3 + x
Solution
a = {0, -3 + x}