(2x+1)(3x+1)=117

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Solution for (2x+1)(3x+1)=117 equation: 


Simplifying
(2x + 1)(3x + 1) = 117

Reorder the terms:
(1 + 2x)(3x + 1) = 117

Reorder the terms:
(1 + 2x)(1 + 3x) = 117

Multiply (1 + 2x) * (1 + 3x)
(1(1 + 3x) + 2x * (1 + 3x)) = 117
((1 * 1 + 3x * 1) + 2x * (1 + 3x)) = 117
((1 + 3x) + 2x * (1 + 3x)) = 117
(1 + 3x + (1 * 2x + 3x * 2x)) = 117
(1 + 3x + (2x + 6x2)) = 117

Combine like terms: 3x + 2x = 5x
(1 + 5x + 6x2) = 117

Solving
1 + 5x + 6x2 = 117

Solving for variable 'x'.

Reorder the terms:
1 + -117 + 5x + 6x2 = 117 + -117

Combine like terms: 1 + -117 = -116
-116 + 5x + 6x2 = 117 + -117

Combine like terms: 117 + -117 = 0
-116 + 5x + 6x2 = 0

Factor a trinomial.
(-29 + -6x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-29 + -6x)' equal to zero and attempt to solve:

Simplifying
-29 + -6x = 0

Solving
-29 + -6x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -6x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -6x = 0 + 29
-6x = 0 + 29

Combine like terms: 0 + 29 = 29
-6x = 29

Divide each side by '-6'.
x = -4.833333333

Simplifying
x = -4.833333333

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-4.833333333, 4}

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