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

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

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

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

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

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

Combine like terms: -6x + 1x = -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 a trinomial.
(1 + -1x)(3 + -2x) = 0

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 + -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
Solution
x = {1, 1.5}