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

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


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

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

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

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

Combine like terms: 1x + 6x = 7x
(2 + 7x + 3x2) = 100

Solving
2 + 7x + 3x2 = 100

Solving for variable 'x'.

Reorder the terms:
2 + -100 + 7x + 3x2 = 100 + -100

Combine like terms: 2 + -100 = -98
-98 + 7x + 3x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-98 + 7x + 3x2 = 0

Factor a trinomial.
(-7 + -1x)(14 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(14 + -3x)' equal to zero and attempt to solve:

Simplifying
14 + -3x = 0

Solving
14 + -3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3x = 0 + -14
-3x = 0 + -14

Combine like terms: 0 + -14 = -14
-3x = -14

Divide each side by '-3'.
x = 4.666666667

Simplifying
x = 4.666666667
Solution
x = {-7, 4.666666667}

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