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

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

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

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

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

Solving
8x + 2x2 = -3 + 3x

Solving for variable 'x'.

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

Combine like terms: 8x + -3x = 5x
3 + 5x + 2x2 = -3 + 3x + 3 + -3x

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

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

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

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

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-1.5, -1}