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

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

Simplifying
4a(a + 2) * x = (a + -2)(b + -3)

Reorder the terms:
4a(2 + a) * x = (a + -2)(b + -3)

Reorder the terms for easier multiplication:
4a * x(2 + a) = (a + -2)(b + -3)

Multiply a * x
4ax(2 + a) = (a + -2)(b + -3)
(2 * 4ax + a * 4ax) = (a + -2)(b + -3)
(8ax + 4a2x) = (a + -2)(b + -3)

Reorder the terms:
8ax + 4a2x = (-2 + a)(b + -3)

Reorder the terms:
8ax + 4a2x = (-2 + a)(-3 + b)

Multiply (-2 + a) * (-3 + b)
8ax + 4a2x = (-2(-3 + b) + a(-3 + b))
8ax + 4a2x = ((-3 * -2 + b * -2) + a(-3 + b))
8ax + 4a2x = ((6 + -2b) + a(-3 + b))
8ax + 4a2x = (6 + -2b + (-3 * a + b * a))
8ax + 4a2x = (6 + -2b + (-3a + ab))

Reorder the terms:
8ax + 4a2x = (6 + -3a + ab + -2b)
8ax + 4a2x = (6 + -3a + ab + -2b)

Solving
8ax + 4a2x = 6 + -3a + ab + -2b

Solving for variable 'a'.

Reorder the terms:
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 6 + -3a + ab + -2b + -6 + 3a + -1ab + 2b

Reorder the terms:
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 6 + -6 + -3a + 3a + ab + -1ab + -2b + 2b

Combine like terms: 6 + -6 = 0
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 0 + -3a + 3a + ab + -1ab + -2b + 2b
-6 + 3a + -1ab + 8ax + 4a2x + 2b = -3a + 3a + ab + -1ab + -2b + 2b

Combine like terms: -3a + 3a = 0
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 0 + ab + -1ab + -2b + 2b
-6 + 3a + -1ab + 8ax + 4a2x + 2b = ab + -1ab + -2b + 2b

Combine like terms: ab + -1ab = 0
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 0 + -2b + 2b
-6 + 3a + -1ab + 8ax + 4a2x + 2b = -2b + 2b

Combine like terms: -2b + 2b = 0
-6 + 3a + -1ab + 8ax + 4a2x + 2b = 0

The solution to this equation could not be determined.