(x+2)(x-5)=-6

Solution for (x+2)(x-5)=-6 equation:

Simplifying
(x + 2)(x + -5) = -6

Reorder the terms:
(2 + x)(x + -5) = -6

Reorder the terms:
(2 + x)(-5 + x) = -6

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = -6
((-5 * 2 + x * 2) + x(-5 + x)) = -6
((-10 + 2x) + x(-5 + x)) = -6
(-10 + 2x + (-5 * x + x * x)) = -6
(-10 + 2x + (-5x + x2)) = -6

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = -6

Solving
-10 + -3x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-10 + 6 + -3x + x2 = -6 + 6

Combine like terms: -10 + 6 = -4
-4 + -3x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-4 + -3x + x2 = 0

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 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 '(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
Solution
x = {-1, 4}