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

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

Simplifying
-3x(1 + x) = -1x(1 + x) + -4
(1 * -3x + x * -3x) = -1x(1 + x) + -4
(-3x + -3x2) = -1x(1 + x) + -4
-3x + -3x2 = (1 * -1x + x * -1x) + -4
-3x + -3x2 = (-1x + -1x2) + -4

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

Solving
-3x + -3x2 = -4 + -1x + -1x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1x + -1x2) = 0

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

Ignore the factor 2.
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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}