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

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


Simplifying
0 = (3x + 1)(2x + 1)

Reorder the terms:
0 = (1 + 3x)(2x + 1)

Reorder the terms:
0 = (1 + 3x)(1 + 2x)

Multiply (1 + 3x) * (1 + 2x)
0 = (1(1 + 2x) + 3x * (1 + 2x))
0 = ((1 * 1 + 2x * 1) + 3x * (1 + 2x))
0 = ((1 + 2x) + 3x * (1 + 2x))
0 = (1 + 2x + (1 * 3x + 2x * 3x))
0 = (1 + 2x + (3x + 6x2))

Combine like terms: 2x + 3x = 5x
0 = (1 + 5x + 6x2)

Solving
0 = 1 + 5x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -5x + -6x2 = 1 + 5x + 6x2 + -1 + -5x + -6x2

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

Combine like terms: 1 + -1 = 0
-1 + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2
-1 + -5x + -6x2 = 5x + -5x + 6x2 + -6x2

Combine like terms: 5x + -5x = 0
-1 + -5x + -6x2 = 0 + 6x2 + -6x2
-1 + -5x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-1 + -5x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 5x + 6x2) = 0

Factor a trinomial.
-1((1 + 2x)(1 + 3x)) = 0

Ignore the factor -1.

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-0.5, -0.3333333333}

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