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

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


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

Reorder the terms:
x(2 + x) = 3x(x + -1) + -3
(2 * x + x * x) = 3x(x + -1) + -3
(2x + x2) = 3x(x + -1) + -3

Reorder the terms:
2x + x2 = 3x(-1 + x) + -3
2x + x2 = (-1 * 3x + x * 3x) + -3
2x + x2 = (-3x + 3x2) + -3

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
3 + 5x + -2x2 = -3 + 3 + -3x + 3x + 3x2 + -3x2

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

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

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

Factor a trinomial.
(3 + -1x)(1 + 2x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, -0.5}

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