(1-x)(2x+6)=0

Solution for (1-x)(2x+6)=0 equation:

Simplifying
(1 + -1x)(2x + 6) = 0

Reorder the terms:
(1 + -1x)(6 + 2x) = 0

Multiply (1 + -1x) * (6 + 2x)
(1(6 + 2x) + -1x * (6 + 2x)) = 0
((6 * 1 + 2x * 1) + -1x * (6 + 2x)) = 0
((6 + 2x) + -1x * (6 + 2x)) = 0
(6 + 2x + (6 * -1x + 2x * -1x)) = 0
(6 + 2x + (-6x + -2x2)) = 0

Combine like terms: 2x + -6x = -4x
(6 + -4x + -2x2) = 0

Solving
6 + -4x + -2x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
2((1 + -1x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {1, -3}