4(x+3)(x-4)-24=2x(x-4)+3(x-2)(x-4)

Solution for 4(x+3)(x-4)-24=2x(x-4)+3(x-2)(x-4) equation:

Simplifying
4(x + 3)(x + -4) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)

Reorder the terms:
4(3 + x)(x + -4) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)

Reorder the terms:
4(3 + x)(-4 + x) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)

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

Combine like terms: 3x + -4x = -1x
4(-12 + -1x + x2) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)
(-12 * 4 + -1x * 4 + x2 * 4) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)
(-48 + -4x + 4x2) + -24 = 2x(x + -4) + 3(x + -2)(x + -4)

Reorder the terms:
-48 + -24 + -4x + 4x2 = 2x(x + -4) + 3(x + -2)(x + -4)

Combine like terms: -48 + -24 = -72
-72 + -4x + 4x2 = 2x(x + -4) + 3(x + -2)(x + -4)

Reorder the terms:
-72 + -4x + 4x2 = 2x(-4 + x) + 3(x + -2)(x + -4)
-72 + -4x + 4x2 = (-4 * 2x + x * 2x) + 3(x + -2)(x + -4)
-72 + -4x + 4x2 = (-8x + 2x2) + 3(x + -2)(x + -4)

Reorder the terms:
-72 + -4x + 4x2 = -8x + 2x2 + 3(-2 + x)(x + -4)

Reorder the terms:
-72 + -4x + 4x2 = -8x + 2x2 + 3(-2 + x)(-4 + x)

Multiply (-2 + x) * (-4 + x)
-72 + -4x + 4x2 = -8x + 2x2 + 3(-2(-4 + x) + x(-4 + x))
-72 + -4x + 4x2 = -8x + 2x2 + 3((-4 * -2 + x * -2) + x(-4 + x))
-72 + -4x + 4x2 = -8x + 2x2 + 3((8 + -2x) + x(-4 + x))
-72 + -4x + 4x2 = -8x + 2x2 + 3(8 + -2x + (-4 * x + x * x))
-72 + -4x + 4x2 = -8x + 2x2 + 3(8 + -2x + (-4x + x2))

Combine like terms: -2x + -4x = -6x
-72 + -4x + 4x2 = -8x + 2x2 + 3(8 + -6x + x2)
-72 + -4x + 4x2 = -8x + 2x2 + (8 * 3 + -6x * 3 + x2 * 3)
-72 + -4x + 4x2 = -8x + 2x2 + (24 + -18x + 3x2)

Reorder the terms:
-72 + -4x + 4x2 = 24 + -8x + -18x + 2x2 + 3x2

Combine like terms: -8x + -18x = -26x
-72 + -4x + 4x2 = 24 + -26x + 2x2 + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
-72 + -4x + 4x2 = 24 + -26x + 5x2

Solving
-72 + -4x + 4x2 = 24 + -26x + 5x2

Solving for variable 'x'.

Reorder the terms:
-72 + -24 + -4x + 26x + 4x2 + -5x2 = 24 + -26x + 5x2 + -24 + 26x + -5x2

Combine like terms: -72 + -24 = -96
-96 + -4x + 26x + 4x2 + -5x2 = 24 + -26x + 5x2 + -24 + 26x + -5x2

Combine like terms: -4x + 26x = 22x
-96 + 22x + 4x2 + -5x2 = 24 + -26x + 5x2 + -24 + 26x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-96 + 22x + -1x2 = 24 + -26x + 5x2 + -24 + 26x + -5x2

Reorder the terms:
-96 + 22x + -1x2 = 24 + -24 + -26x + 26x + 5x2 + -5x2

Combine like terms: 24 + -24 = 0
-96 + 22x + -1x2 = 0 + -26x + 26x + 5x2 + -5x2
-96 + 22x + -1x2 = -26x + 26x + 5x2 + -5x2

Combine like terms: -26x + 26x = 0
-96 + 22x + -1x2 = 0 + 5x2 + -5x2
-96 + 22x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-96 + 22x + -1x2 = 0

Factor a trinomial.
(-16 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-16 + x)' equal to zero and attempt to solve:

Simplifying
-16 + x = 0

Solving
-16 + x = 0

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

Add '16' to each side of the equation.
-16 + 16 + x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x = 0 + 16
x = 0 + 16

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {16, 6}