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

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


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

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

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

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

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

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

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

Multiply (8 + x) * (-3 + x)
-24 + -6x + 3x2 = (8(-3 + x) + x(-3 + x))
-24 + -6x + 3x2 = ((-3 * 8 + x * 8) + x(-3 + x))
-24 + -6x + 3x2 = ((-24 + 8x) + x(-3 + x))
-24 + -6x + 3x2 = (-24 + 8x + (-3 * x + x * x))
-24 + -6x + 3x2 = (-24 + 8x + (-3x + x2))

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

Add '24' to each side of the equation.
-24 + -6x + 24 + 3x2 = -24 + 5x + 24 + x2

Reorder the terms:
-24 + 24 + -6x + 3x2 = -24 + 5x + 24 + x2

Combine like terms: -24 + 24 = 0
0 + -6x + 3x2 = -24 + 5x + 24 + x2
-6x + 3x2 = -24 + 5x + 24 + x2

Reorder the terms:
-6x + 3x2 = -24 + 24 + 5x + x2

Combine like terms: -24 + 24 = 0
-6x + 3x2 = 0 + 5x + x2
-6x + 3x2 = 5x + x2

Solving
-6x + 3x2 = 5x + x2

Solving for variable 'x'.

Reorder the terms:
-6x + -5x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2

Combine like terms: -6x + -5x = -11x
-11x + 3x2 + -1x2 = 5x + x2 + -5x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-11x + 2x2 = 5x + x2 + -5x + -1x2

Reorder the terms:
-11x + 2x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
-11x + 2x2 = 0 + x2 + -1x2
-11x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-11 + 2x) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-11 + 2x)' equal to zero and attempt to solve:

Simplifying
-11 + 2x = 0

Solving
-11 + 2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2x = 0 + 11
2x = 0 + 11

Combine like terms: 0 + 11 = 11
2x = 11

Divide each side by '2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {0, 5.5}

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