(x+3)(x-4)=-6

Solution for (x+3)(x-4)=-6 equation:

Simplifying
(x + 3)(x + -4) = -6

Reorder the terms:
(3 + x)(x + -4) = -6

Reorder the terms:
(3 + x)(-4 + x) = -6

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = -6
((-4 * 3 + x * 3) + x(-4 + x)) = -6
((-12 + 3x) + x(-4 + x)) = -6
(-12 + 3x + (-4 * x + x * x)) = -6
(-12 + 3x + (-4x + x2)) = -6

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = -6

Solving
-12 + -1x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-12 + 6 + -1x + x2 = -6 + 6

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

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

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
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 = {-2, 3}