(x+1)(3x)=(x+1)(24)

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Solution for (x+1)(3x)=(x+1)(24) equation: 


Simplifying
(x + 1)(3x) = (x + 1)(24)

Reorder the terms:
(1 + x)(3x) = (x + 1)(24)

Remove parenthesis around (3x)
(1 + x) * 3x = (x + 1)(24)

Reorder the terms for easier multiplication:
3x(1 + x) = (x + 1)(24)
(1 * 3x + x * 3x) = (x + 1)(24)
(3x + 3x2) = (x + 1)(24)

Reorder the terms:
3x + 3x2 = (1 + x)(24)

Reorder the terms for easier multiplication:
3x + 3x2 = 24(1 + x)
3x + 3x2 = (1 * 24 + x * 24)
3x + 3x2 = (24 + 24x)

Solving
3x + 3x2 = 24 + 24x

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 8}

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