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

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


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

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

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

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

Combine like terms: -4x + 2x = -2x
(-8 + -2x + x2) = 4x(x + -3)

Reorder the terms:
-8 + -2x + x2 = 4x(-3 + x)
-8 + -2x + x2 = (-3 * 4x + x * 4x)
-8 + -2x + x2 = (-12x + 4x2)

Solving
-8 + -2x + x2 = -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
-8 + -2x + 12x + x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: -2x + 12x = 10x
-8 + 10x + x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: x2 + -4x2 = -3x2
-8 + 10x + -3x2 = -12x + 4x2 + 12x + -4x2

Reorder the terms:
-8 + 10x + -3x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
-8 + 10x + -3x2 = 0 + 4x2 + -4x2
-8 + 10x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-8 + 10x + -3x2 = 0

Factor a trinomial.
(-2 + x)(4 + -3x) = 0


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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {2, 1.333333333}

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