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

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

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

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

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

Multiply (-2 + x) * (3 + 2x)
(-2(3 + 2x) + x(3 + 2x)) = -6
((3 * -2 + 2x * -2) + x(3 + 2x)) = -6
((-6 + -4x) + x(3 + 2x)) = -6
(-6 + -4x + (3 * x + 2x * x)) = -6
(-6 + -4x + (3x + 2x2)) = -6

Combine like terms: -4x + 3x = -1x
(-6 + -1x + 2x2) = -6

Add '6' to each side of the equation.
-6 + -1x + 6 + 2x2 = -6 + 6

Reorder the terms:
-6 + 6 + -1x + 2x2 = -6 + 6

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

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

Solving
-1x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
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
Solution
x = {0, 0.5}