6+(x-5)(x+2)=0

Solution for 6+(x-5)(x+2)=0 equation:

Simplifying
6 + (x + -5)(x + 2) = 0

Reorder the terms:
6 + (-5 + x)(x + 2) = 0

Reorder the terms:
6 + (-5 + x)(2 + x) = 0

Multiply (-5 + x) * (2 + x)
6 + (-5(2 + x) + x(2 + x)) = 0
6 + ((2 * -5 + x * -5) + x(2 + x)) = 0
6 + ((-10 + -5x) + x(2 + x)) = 0
6 + (-10 + -5x + (2 * x + x * x)) = 0
6 + (-10 + -5x + (2x + x2)) = 0

Combine like terms: -5x + 2x = -3x
6 + (-10 + -3x + x2) = 0

Combine like terms: 6 + -10 = -4
-4 + -3x + x2 = 0

Solving
-4 + -3x + x2 = 0

Solving for variable 'x'.

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}