(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.
(-3 + -1x)(1 + -1x) = 0

Subproblem 1
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
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 = {-3, 1}