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

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

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

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

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

Solving
3 + -1x + -2x2 = -3

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(3 + -2x)(2 + 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 '(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 = {1.5, -2}