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

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

Simplifying
6 + -1(x + 2)(x + -3) = 0

Reorder the terms:
6 + -1(2 + x)(x + -3) = 0

Reorder the terms:
6 + -1(2 + x)(-3 + x) = 0

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

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

Combine like terms: 6 + 6 = 12
12 + 1x + -1x2 = 0

Solving
12 + 1x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, -3}