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

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


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

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

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

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

Combine like terms: 5x + -2x = 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.
(-4 + -1x)(1 + -1x) = 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 '(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
Solution
x = {-4, 1}

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