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

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


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

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

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

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

Combine like terms: 7x + -3x = 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 = -45
-45 + 4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-9, 5}

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