X^2+3x-24=
x
2
+3x−24=
\,\,3x+1
3x+1

x = -8

Step-by-step explanation:

Solve for x:

3 (x + 8) = 2 (3 x + 24)

Expand out terms of the left hand side:

3 x + 24 = 2 (3 x + 24)

Expand out terms of the right hand side:

3 x + 24 = 6 x + 48

Subtract 6 x from both sides:

(3 x - 6 x) + 24 = (6 x - 6 x) + 48

3 x - 6 x = -3 x:

-3 x + 24 = (6 x - 6 x) + 48

6 x - 6 x = 0:

24 - 3 x = 48

Subtract 24 from both sides:

(24 - 24) - 3 x = 48 - 24

24 - 24 = 0:

-3 x = 48 - 24

48 - 24 = 24:

-3 x = 24

Divide both sides of -3 x = 24 by -3:

(-3 x)/(-3) = 24/(-3)

(-3)/(-3) = 1:

x = 24/(-3)

The gcd of 24 and -3 is 3, so 24/(-3) = (3×8)/(3 (-1)) = 3/3×8/(-1) = 8/(-1):

x = 8/(-1)

Multiply numerator and denominator of 8/(-1) by -1:

x = -8

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step-by-step explanation: