(3x+1)(x-1)=15

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Solution for (3x+1)(x-1)=15 equation: 


Simplifying
(3x + 1)(x + -1) = 15

Reorder the terms:
(1 + 3x)(x + -1) = 15

Reorder the terms:
(1 + 3x)(-1 + x) = 15

Multiply (1 + 3x) * (-1 + x)
(1(-1 + x) + 3x * (-1 + x)) = 15
((-1 * 1 + x * 1) + 3x * (-1 + x)) = 15
((-1 + 1x) + 3x * (-1 + x)) = 15
(-1 + 1x + (-1 * 3x + x * 3x)) = 15
(-1 + 1x + (-3x + 3x2)) = 15

Combine like terms: 1x + -3x = -2x
(-1 + -2x + 3x2) = 15

Solving
-1 + -2x + 3x2 = 15

Solving for variable 'x'.

Reorder the terms:
-1 + -15 + -2x + 3x2 = 15 + -15

Combine like terms: -1 + -15 = -16
-16 + -2x + 3x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-16 + -2x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -3x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-2, 2.666666667}

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