3x(x+7)=24

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

Simplifying
3x(x + 7) = 24

Reorder the terms:
3x(7 + x) = 24
(7 * 3x + x * 3x) = 24
(21x + 3x2) = 24

Solving
21x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 21x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 7x + x2) = 0

Factor a trinomial.
3((-8 + -1x)(1 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 1}