(x-15)*(x+8)=24

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Solution for (x-15)*(x+8)=24 equation: 


Simplifying
(x + -15)(x + 8) = 24

Reorder the terms:
(-15 + x)(x + 8) = 24

Reorder the terms:
(-15 + x)(8 + x) = 24

Multiply (-15 + x) * (8 + x)
(-15(8 + x) + x(8 + x)) = 24
((8 * -15 + x * -15) + x(8 + x)) = 24
((-120 + -15x) + x(8 + x)) = 24
(-120 + -15x + (8 * x + x * x)) = 24
(-120 + -15x + (8x + x2)) = 24

Combine like terms: -15x + 8x = -7x
(-120 + -7x + x2) = 24

Solving
-120 + -7x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-120 + -24 + -7x + x2 = 24 + -24

Combine like terms: -120 + -24 = -144
-144 + -7x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-144 + -7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(16 + -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 '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-9, 16}

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