(3x+1)(x+1)=40

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Solution for (3x+1)(x+1)=40 equation: 


Simplifying
(3x + 1)(x + 1) = 40

Reorder the terms:
(1 + 3x)(x + 1) = 40

Reorder the terms:
(1 + 3x)(1 + x) = 40

Multiply (1 + 3x) * (1 + x)
(1(1 + x) + 3x * (1 + x)) = 40
((1 * 1 + x * 1) + 3x * (1 + x)) = 40
((1 + 1x) + 3x * (1 + x)) = 40
(1 + 1x + (1 * 3x + x * 3x)) = 40
(1 + 1x + (3x + 3x2)) = 40

Combine like terms: 1x + 3x = 4x
(1 + 4x + 3x2) = 40

Solving
1 + 4x + 3x2 = 40

Solving for variable 'x'.

Reorder the terms:
1 + -40 + 4x + 3x2 = 40 + -40

Combine like terms: 1 + -40 = -39
-39 + 4x + 3x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-39 + 4x + 3x2 = 0

Factor a trinomial.
(-13 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4.333333333, 3}

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