4(x+3)(x+2)-3(3x+6)(x+2)=8(x+2)(3x+6)

Solution for 4(x+3)(x+2)-3(3x+6)(x+2)=8(x+2)(3x+6) equation:

Simplifying
4(x + 3)(x + 2) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)

Reorder the terms:
4(3 + x)(x + 2) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)

Reorder the terms:
4(3 + x)(2 + x) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)

Multiply (3 + x) * (2 + x)
4(3(2 + x) + x(2 + x)) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
4((2 * 3 + x * 3) + x(2 + x)) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
4((6 + 3x) + x(2 + x)) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
4(6 + 3x + (2 * x + x * x)) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
4(6 + 3x + (2x + x2)) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)

Combine like terms: 3x + 2x = 5x
4(6 + 5x + x2) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
(6 * 4 + 5x * 4 + x2 * 4) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)
(24 + 20x + 4x2) + -3(3x + 6)(x + 2) = 8(x + 2)(3x + 6)

Reorder the terms:
24 + 20x + 4x2 + -3(6 + 3x)(x + 2) = 8(x + 2)(3x + 6)

Reorder the terms:
24 + 20x + 4x2 + -3(6 + 3x)(2 + x) = 8(x + 2)(3x + 6)

Multiply (6 + 3x) * (2 + x)
24 + 20x + 4x2 + -3(6(2 + x) + 3x * (2 + x)) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + -3((2 * 6 + x * 6) + 3x * (2 + x)) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + -3((12 + 6x) + 3x * (2 + x)) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + -3(12 + 6x + (2 * 3x + x * 3x)) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + -3(12 + 6x + (6x + 3x2)) = 8(x + 2)(3x + 6)

Combine like terms: 6x + 6x = 12x
24 + 20x + 4x2 + -3(12 + 12x + 3x2) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + (12 * -3 + 12x * -3 + 3x2 * -3) = 8(x + 2)(3x + 6)
24 + 20x + 4x2 + (-36 + -36x + -9x2) = 8(x + 2)(3x + 6)

Reorder the terms:
24 + -36 + 20x + -36x + 4x2 + -9x2 = 8(x + 2)(3x + 6)

Combine like terms: 24 + -36 = -12
-12 + 20x + -36x + 4x2 + -9x2 = 8(x + 2)(3x + 6)

Combine like terms: 20x + -36x = -16x
-12 + -16x + 4x2 + -9x2 = 8(x + 2)(3x + 6)

Combine like terms: 4x2 + -9x2 = -5x2
-12 + -16x + -5x2 = 8(x + 2)(3x + 6)

Reorder the terms:
-12 + -16x + -5x2 = 8(2 + x)(3x + 6)

Reorder the terms:
-12 + -16x + -5x2 = 8(2 + x)(6 + 3x)

Multiply (2 + x) * (6 + 3x)
-12 + -16x + -5x2 = 8(2(6 + 3x) + x(6 + 3x))
-12 + -16x + -5x2 = 8((6 * 2 + 3x * 2) + x(6 + 3x))
-12 + -16x + -5x2 = 8((12 + 6x) + x(6 + 3x))
-12 + -16x + -5x2 = 8(12 + 6x + (6 * x + 3x * x))
-12 + -16x + -5x2 = 8(12 + 6x + (6x + 3x2))

Combine like terms: 6x + 6x = 12x
-12 + -16x + -5x2 = 8(12 + 12x + 3x2)
-12 + -16x + -5x2 = (12 * 8 + 12x * 8 + 3x2 * 8)
-12 + -16x + -5x2 = (96 + 96x + 24x2)

Solving
-12 + -16x + -5x2 = 96 + 96x + 24x2

Solving for variable 'x'.

Reorder the terms:
-12 + -96 + -16x + -96x + -5x2 + -24x2 = 96 + 96x + 24x2 + -96 + -96x + -24x2

Combine like terms: -12 + -96 = -108
-108 + -16x + -96x + -5x2 + -24x2 = 96 + 96x + 24x2 + -96 + -96x + -24x2

Combine like terms: -16x + -96x = -112x
-108 + -112x + -5x2 + -24x2 = 96 + 96x + 24x2 + -96 + -96x + -24x2

Combine like terms: -5x2 + -24x2 = -29x2
-108 + -112x + -29x2 = 96 + 96x + 24x2 + -96 + -96x + -24x2

Reorder the terms:
-108 + -112x + -29x2 = 96 + -96 + 96x + -96x + 24x2 + -24x2

Combine like terms: 96 + -96 = 0
-108 + -112x + -29x2 = 0 + 96x + -96x + 24x2 + -24x2
-108 + -112x + -29x2 = 96x + -96x + 24x2 + -24x2

Combine like terms: 96x + -96x = 0
-108 + -112x + -29x2 = 0 + 24x2 + -24x2
-108 + -112x + -29x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-108 + -112x + -29x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(108 + 112x + 29x2) = 0

Factor a trinomial.
-1((2 + x)(54 + 29x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(54 + 29x)' equal to zero and attempt to solve:

Simplifying
54 + 29x = 0

Solving
54 + 29x = 0

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

Add '-54' to each side of the equation.
54 + -54 + 29x = 0 + -54

Combine like terms: 54 + -54 = 0
0 + 29x = 0 + -54
29x = 0 + -54

Combine like terms: 0 + -54 = -54
29x = -54

Divide each side by '29'.
x = -1.862068966

Simplifying
x = -1.862068966
Solution
x = {-2, -1.862068966}