(x+4)(x-6)=-21

Solution for (x+4)(x-6)=-21 equation:

Simplifying
(x + 4)(x + -6) = -21

Reorder the terms:
(4 + x)(x + -6) = -21

Reorder the terms:
(4 + x)(-6 + x) = -21

Multiply (4 + x) * (-6 + x)
(4(-6 + x) + x(-6 + x)) = -21
((-6 * 4 + x * 4) + x(-6 + x)) = -21
((-24 + 4x) + x(-6 + x)) = -21
(-24 + 4x + (-6 * x + x * x)) = -21
(-24 + 4x + (-6x + x2)) = -21

Combine like terms: 4x + -6x = -2x
(-24 + -2x + x2) = -21

Solving
-24 + -2x + x2 = -21

Solving for variable 'x'.

Reorder the terms:
-24 + 21 + -2x + x2 = -21 + 21

Combine like terms: -24 + 21 = -3
-3 + -2x + x2 = -21 + 21

Combine like terms: -21 + 21 = 0
-3 + -2x + x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -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 '(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 = {-1, 3}