(-3x+1)(x-4)-2x(x-4)=0

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Solution for (-3x+1)(x-4)-2x(x-4)=0 equation: 


Simplifying
(-3x + 1)(x + -4) + -2x(x + -4) = 0

Reorder the terms:
(1 + -3x)(x + -4) + -2x(x + -4) = 0

Reorder the terms:
(1 + -3x)(-4 + x) + -2x(x + -4) = 0

Multiply (1 + -3x) * (-4 + x)
(1(-4 + x) + -3x * (-4 + x)) + -2x(x + -4) = 0
((-4 * 1 + x * 1) + -3x * (-4 + x)) + -2x(x + -4) = 0
((-4 + 1x) + -3x * (-4 + x)) + -2x(x + -4) = 0
(-4 + 1x + (-4 * -3x + x * -3x)) + -2x(x + -4) = 0
(-4 + 1x + (12x + -3x2)) + -2x(x + -4) = 0

Combine like terms: 1x + 12x = 13x
(-4 + 13x + -3x2) + -2x(x + -4) = 0

Reorder the terms:
-4 + 13x + -3x2 + -2x(-4 + x) = 0
-4 + 13x + -3x2 + (-4 * -2x + x * -2x) = 0
-4 + 13x + -3x2 + (8x + -2x2) = 0

Reorder the terms:
-4 + 13x + 8x + -3x2 + -2x2 = 0

Combine like terms: 13x + 8x = 21x
-4 + 21x + -3x2 + -2x2 = 0

Combine like terms: -3x2 + -2x2 = -5x2
-4 + 21x + -5x2 = 0

Solving
-4 + 21x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + x)(1 + -5x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {4, 0.2}

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