(1-2x)(x+3)=6

Solution for (1-2x)(x+3)=6 equation:

Simplifying
(1 + -2x)(x + 3) = 6

Reorder the terms:
(1 + -2x)(3 + x) = 6

Multiply (1 + -2x) * (3 + x)
(1(3 + x) + -2x * (3 + x)) = 6
((3 * 1 + x * 1) + -2x * (3 + x)) = 6
((3 + 1x) + -2x * (3 + x)) = 6
(3 + 1x + (3 * -2x + x * -2x)) = 6
(3 + 1x + (-6x + -2x2)) = 6

Combine like terms: 1x + -6x = -5x
(3 + -5x + -2x2) = 6

Solving
3 + -5x + -2x2 = 6

Solving for variable 'x'.

Reorder the terms:
3 + -6 + -5x + -2x2 = 6 + -6

Combine like terms: 3 + -6 = -3
-3 + -5x + -2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-3 + -5x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 5x + 2x2) = 0

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

Ignore the factor -1.
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}