(x-3)(x+7)=-24

Solution for (x-3)(x+7)=-24 equation:

Simplifying
(x + -3)(x + 7) = -24

Reorder the terms:
(-3 + x)(x + 7) = -24

Reorder the terms:
(-3 + x)(7 + x) = -24

Multiply (-3 + x) * (7 + x)
(-3(7 + x) + x(7 + x)) = -24
((7 * -3 + x * -3) + x(7 + x)) = -24
((-21 + -3x) + x(7 + x)) = -24
(-21 + -3x + (7 * x + x * x)) = -24
(-21 + -3x + (7x + x2)) = -24

Combine like terms: -3x + 7x = 4x
(-21 + 4x + x2) = -24

Solving
-21 + 4x + x2 = -24

Solving for variable 'x'.

Reorder the terms:
-21 + 24 + 4x + x2 = -24 + 24

Combine like terms: -21 + 24 = 3
3 + 4x + x2 = -24 + 24

Combine like terms: -24 + 24 = 0
3 + 4x + x2 = 0

Factor a trinomial.
(3 + x)(1 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-3, -1}