(2x+a)(x-4)=3(x+a)-2(x+5)(6-x)

Solution for (2x+a)(x-4)=3(x+a)-2(x+5)(6-x) equation:

Simplifying
(2x + a)(x + -4) = 3(x + a) + -2(x + 5)(6 + -1x)

Reorder the terms:
(a + 2x)(x + -4) = 3(x + a) + -2(x + 5)(6 + -1x)

Reorder the terms:
(a + 2x)(-4 + x) = 3(x + a) + -2(x + 5)(6 + -1x)

Multiply (a + 2x) * (-4 + x)
(a(-4 + x) + 2x * (-4 + x)) = 3(x + a) + -2(x + 5)(6 + -1x)
((-4 * a + x * a) + 2x * (-4 + x)) = 3(x + a) + -2(x + 5)(6 + -1x)
((-4a + ax) + 2x * (-4 + x)) = 3(x + a) + -2(x + 5)(6 + -1x)
(-4a + ax + (-4 * 2x + x * 2x)) = 3(x + a) + -2(x + 5)(6 + -1x)
(-4a + ax + (-8x + 2x2)) = 3(x + a) + -2(x + 5)(6 + -1x)
(-4a + ax + -8x + 2x2) = 3(x + a) + -2(x + 5)(6 + -1x)

Reorder the terms:
-4a + ax + -8x + 2x2 = 3(a + x) + -2(x + 5)(6 + -1x)
-4a + ax + -8x + 2x2 = (a * 3 + x * 3) + -2(x + 5)(6 + -1x)
-4a + ax + -8x + 2x2 = (3a + 3x) + -2(x + 5)(6 + -1x)

Reorder the terms:
-4a + ax + -8x + 2x2 = 3a + 3x + -2(5 + x)(6 + -1x)

Multiply (5 + x) * (6 + -1x)
-4a + ax + -8x + 2x2 = 3a + 3x + -2(5(6 + -1x) + x(6 + -1x))
-4a + ax + -8x + 2x2 = 3a + 3x + -2((6 * 5 + -1x * 5) + x(6 + -1x))
-4a + ax + -8x + 2x2 = 3a + 3x + -2((30 + -5x) + x(6 + -1x))
-4a + ax + -8x + 2x2 = 3a + 3x + -2(30 + -5x + (6 * x + -1x * x))
-4a + ax + -8x + 2x2 = 3a + 3x + -2(30 + -5x + (6x + -1x2))

Combine like terms: -5x + 6x = 1x
-4a + ax + -8x + 2x2 = 3a + 3x + -2(30 + 1x + -1x2)
-4a + ax + -8x + 2x2 = 3a + 3x + (30 * -2 + 1x * -2 + -1x2 * -2)
-4a + ax + -8x + 2x2 = 3a + 3x + (-60 + -2x + 2x2)

Reorder the terms:
-4a + ax + -8x + 2x2 = -60 + 3a + 3x + -2x + 2x2

Combine like terms: 3x + -2x = 1x
-4a + ax + -8x + 2x2 = -60 + 3a + 1x + 2x2

Add '-2x2' to each side of the equation.
-4a + ax + -8x + 2x2 + -2x2 = -60 + 3a + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4a + ax + -8x + 0 = -60 + 3a + 1x + 2x2 + -2x2
-4a + ax + -8x = -60 + 3a + 1x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4a + ax + -8x = -60 + 3a + 1x + 0
-4a + ax + -8x = -60 + 3a + 1x

Solving
-4a + ax + -8x = -60 + 3a + 1x

Solving for variable 'a'.

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

Add '-3a' to each side of the equation.
-4a + ax + -3a + -8x = -60 + 3a + -3a + 1x

Reorder the terms:
-4a + -3a + ax + -8x = -60 + 3a + -3a + 1x

Combine like terms: -4a + -3a = -7a
-7a + ax + -8x = -60 + 3a + -3a + 1x

Combine like terms: 3a + -3a = 0
-7a + ax + -8x = -60 + 0 + 1x
-7a + ax + -8x = -60 + 1x

Add '8x' to each side of the equation.
-7a + ax + -8x + 8x = -60 + 1x + 8x

Combine like terms: -8x + 8x = 0
-7a + ax + 0 = -60 + 1x + 8x
-7a + ax = -60 + 1x + 8x

Combine like terms: 1x + 8x = 9x
-7a + ax = -60 + 9x

Reorder the terms:
60 + -7a + ax + -9x = -60 + 9x + 60 + -9x

Reorder the terms:
60 + -7a + ax + -9x = -60 + 60 + 9x + -9x

Combine like terms: -60 + 60 = 0
60 + -7a + ax + -9x = 0 + 9x + -9x
60 + -7a + ax + -9x = 9x + -9x

Combine like terms: 9x + -9x = 0
60 + -7a + ax + -9x = 0

The solution to this equation could not be determined.