(3x+2)(x+1)=10

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Solution for (3x+2)(x+1)=10 equation: 


Simplifying
(3x + 2)(x + 1) = 10

Reorder the terms:
(2 + 3x)(x + 1) = 10

Reorder the terms:
(2 + 3x)(1 + x) = 10

Multiply (2 + 3x) * (1 + x)
(2(1 + x) + 3x * (1 + x)) = 10
((1 * 2 + x * 2) + 3x * (1 + x)) = 10
((2 + 2x) + 3x * (1 + x)) = 10
(2 + 2x + (1 * 3x + x * 3x)) = 10
(2 + 2x + (3x + 3x2)) = 10

Combine like terms: 2x + 3x = 5x
(2 + 5x + 3x2) = 10

Solving
2 + 5x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
2 + -10 + 5x + 3x2 = 10 + -10

Combine like terms: 2 + -10 = -8
-8 + 5x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-8 + 5x + 3x2 = 0

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


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

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 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 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

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 = {-2.666666667, 1}

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