(2x+1)(3x+1)=100

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Solution for (2x+1)(3x+1)=100 equation: 


Simplifying
(2x + 1)(3x + 1) = 100

Reorder the terms:
(1 + 2x)(3x + 1) = 100

Reorder the terms:
(1 + 2x)(1 + 3x) = 100

Multiply (1 + 2x) * (1 + 3x)
(1(1 + 3x) + 2x * (1 + 3x)) = 100
((1 * 1 + 3x * 1) + 2x * (1 + 3x)) = 100
((1 + 3x) + 2x * (1 + 3x)) = 100
(1 + 3x + (1 * 2x + 3x * 2x)) = 100
(1 + 3x + (2x + 6x2)) = 100

Combine like terms: 3x + 2x = 5x
(1 + 5x + 6x2) = 100

Solving
1 + 5x + 6x2 = 100

Solving for variable 'x'.

Reorder the terms:
1 + -100 + 5x + 6x2 = 100 + -100

Combine like terms: 1 + -100 = -99
-99 + 5x + 6x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-99 + 5x + 6x2 = 0

Factor a trinomial.
(-9 + -2x)(11 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
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
Solution
x = {-4.5, 3.666666667}

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