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

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

Simplifying
0 = (1 + 2x)(3 + -1x)

Multiply (1 + 2x) * (3 + -1x)
0 = (1(3 + -1x) + 2x * (3 + -1x))
0 = ((3 * 1 + -1x * 1) + 2x * (3 + -1x))
0 = ((3 + -1x) + 2x * (3 + -1x))
0 = (3 + -1x + (3 * 2x + -1x * 2x))
0 = (3 + -1x + (6x + -2x2))

Combine like terms: -1x + 6x = 5x
0 = (3 + 5x + -2x2)

Solving
0 = 3 + 5x + -2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}