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

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


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

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

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

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

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

Reorder the terms:
-4 + 3x + x2 = 3x(-2 + x)
-4 + 3x + x2 = (-2 * 3x + x * 3x)
-4 + 3x + x2 = (-6x + 3x2)

Solving
-4 + 3x + x2 = -6x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4 + 3x + 6x + x2 + -3x2 = -6x + 3x2 + 6x + -3x2

Combine like terms: 3x + 6x = 9x
-4 + 9x + x2 + -3x2 = -6x + 3x2 + 6x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-4 + 9x + -2x2 = -6x + 3x2 + 6x + -3x2

Reorder the terms:
-4 + 9x + -2x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
-4 + 9x + -2x2 = 0 + 3x2 + -3x2
-4 + 9x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + 9x + -2x2 = 0

Factor a trinomial.
(-4 + x)(1 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {4, 0.5}

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