(x+1)(3x+2)=24

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Solution for (x+1)(3x+2)=24 equation: 


Simplifying
(x + 1)(3x + 2) = 24

Reorder the terms:
(1 + x)(3x + 2) = 24

Reorder the terms:
(1 + x)(2 + 3x) = 24

Multiply (1 + x) * (2 + 3x)
(1(2 + 3x) + x(2 + 3x)) = 24
((2 * 1 + 3x * 1) + x(2 + 3x)) = 24
((2 + 3x) + x(2 + 3x)) = 24
(2 + 3x + (2 * x + 3x * x)) = 24
(2 + 3x + (2x + 3x2)) = 24

Combine like terms: 3x + 2x = 5x
(2 + 5x + 3x2) = 24

Solving
2 + 5x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
2 + -24 + 5x + 3x2 = 24 + -24

Combine like terms: 2 + -24 = -22
-22 + 5x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-22 + 5x + 3x2 = 0

Factor a trinomial.
(-11 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3.666666667, 2}

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