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

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


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

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

Remove parenthesis around (2x)
3x + x2 = 2x(x + 3) + -4

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

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

Solving
3x + x2 = -4 + 6x + 2x2

Solving for variable 'x'.

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

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

Combine like terms: x2 + -2x2 = -1x2
4 + -3x + -1x2 = -4 + 6x + 2x2 + 4 + -6x + -2x2

Reorder the terms:
4 + -3x + -1x2 = -4 + 4 + 6x + -6x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
4 + -3x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
4 + -3x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
4 + -3x + -1x2 = 0 + 2x2 + -2x2
4 + -3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + -3x + -1x2 = 0

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


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, -4}

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