(x-4)*(3x-7)=(x-2)*(3x+8)

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Solution for (x-4)*(3x-7)=(x-2)*(3x+8) equation: 


Simplifying
(x + -4)(3x + -7) = (x + -2)(3x + 8)

Reorder the terms:
(-4 + x)(3x + -7) = (x + -2)(3x + 8)

Reorder the terms:
(-4 + x)(-7 + 3x) = (x + -2)(3x + 8)

Multiply (-4 + x) * (-7 + 3x)
(-4(-7 + 3x) + x(-7 + 3x)) = (x + -2)(3x + 8)
((-7 * -4 + 3x * -4) + x(-7 + 3x)) = (x + -2)(3x + 8)
((28 + -12x) + x(-7 + 3x)) = (x + -2)(3x + 8)
(28 + -12x + (-7 * x + 3x * x)) = (x + -2)(3x + 8)
(28 + -12x + (-7x + 3x2)) = (x + -2)(3x + 8)

Combine like terms: -12x + -7x = -19x
(28 + -19x + 3x2) = (x + -2)(3x + 8)

Reorder the terms:
28 + -19x + 3x2 = (-2 + x)(3x + 8)

Reorder the terms:
28 + -19x + 3x2 = (-2 + x)(8 + 3x)

Multiply (-2 + x) * (8 + 3x)
28 + -19x + 3x2 = (-2(8 + 3x) + x(8 + 3x))
28 + -19x + 3x2 = ((8 * -2 + 3x * -2) + x(8 + 3x))
28 + -19x + 3x2 = ((-16 + -6x) + x(8 + 3x))
28 + -19x + 3x2 = (-16 + -6x + (8 * x + 3x * x))
28 + -19x + 3x2 = (-16 + -6x + (8x + 3x2))

Combine like terms: -6x + 8x = 2x
28 + -19x + 3x2 = (-16 + 2x + 3x2)

Add '-3x2' to each side of the equation.
28 + -19x + 3x2 + -3x2 = -16 + 2x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
28 + -19x + 0 = -16 + 2x + 3x2 + -3x2
28 + -19x = -16 + 2x + 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
28 + -19x = -16 + 2x + 0
28 + -19x = -16 + 2x

Solving
28 + -19x = -16 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
28 + -19x + -2x = -16 + 2x + -2x

Combine like terms: -19x + -2x = -21x
28 + -21x = -16 + 2x + -2x

Combine like terms: 2x + -2x = 0
28 + -21x = -16 + 0
28 + -21x = -16

Add '-28' to each side of the equation.
28 + -28 + -21x = -16 + -28

Combine like terms: 28 + -28 = 0
0 + -21x = -16 + -28
-21x = -16 + -28

Combine like terms: -16 + -28 = -44
-21x = -44

Divide each side by '-21'.
x = 2.095238095

Simplifying
x = 2.095238095

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