(3x+5)(x+1)=120

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Solution for (3x+5)(x+1)=120 equation: 


Simplifying
(3x + 5)(x + 1) = 120

Reorder the terms:
(5 + 3x)(x + 1) = 120

Reorder the terms:
(5 + 3x)(1 + x) = 120

Multiply (5 + 3x) * (1 + x)
(5(1 + x) + 3x * (1 + x)) = 120
((1 * 5 + x * 5) + 3x * (1 + x)) = 120
((5 + 5x) + 3x * (1 + x)) = 120
(5 + 5x + (1 * 3x + x * 3x)) = 120
(5 + 5x + (3x + 3x2)) = 120

Combine like terms: 5x + 3x = 8x
(5 + 8x + 3x2) = 120

Solving
5 + 8x + 3x2 = 120

Solving for variable 'x'.

Reorder the terms:
5 + -120 + 8x + 3x2 = 120 + -120

Combine like terms: 5 + -120 = -115
-115 + 8x + 3x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-115 + 8x + 3x2 = 0

Factor a trinomial.
(-23 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-23 + -3x)' equal to zero and attempt to solve:

Simplifying
-23 + -3x = 0

Solving
-23 + -3x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -3x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -3x = 0 + 23
-3x = 0 + 23

Combine like terms: 0 + 23 = 23
-3x = 23

Divide each side by '-3'.
x = -7.666666667

Simplifying
x = -7.666666667

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 = {-7.666666667, 5}

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