(3x+1)(x-3)=2+3(x+5)

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Solution for (3x+1)(x-3)=2+3(x+5) equation: 


Simplifying
(3x + 1)(x + -3) = 2 + 3(x + 5)

Reorder the terms:
(1 + 3x)(x + -3) = 2 + 3(x + 5)

Reorder the terms:
(1 + 3x)(-3 + x) = 2 + 3(x + 5)

Multiply (1 + 3x) * (-3 + x)
(1(-3 + x) + 3x * (-3 + x)) = 2 + 3(x + 5)
((-3 * 1 + x * 1) + 3x * (-3 + x)) = 2 + 3(x + 5)
((-3 + 1x) + 3x * (-3 + x)) = 2 + 3(x + 5)
(-3 + 1x + (-3 * 3x + x * 3x)) = 2 + 3(x + 5)
(-3 + 1x + (-9x + 3x2)) = 2 + 3(x + 5)

Combine like terms: 1x + -9x = -8x
(-3 + -8x + 3x2) = 2 + 3(x + 5)

Reorder the terms:
-3 + -8x + 3x2 = 2 + 3(5 + x)
-3 + -8x + 3x2 = 2 + (5 * 3 + x * 3)
-3 + -8x + 3x2 = 2 + (15 + 3x)

Combine like terms: 2 + 15 = 17
-3 + -8x + 3x2 = 17 + 3x

Solving
-3 + -8x + 3x2 = 17 + 3x

Solving for variable 'x'.

Reorder the terms:
-3 + -17 + -8x + -3x + 3x2 = 17 + 3x + -17 + -3x

Combine like terms: -3 + -17 = -20
-20 + -8x + -3x + 3x2 = 17 + 3x + -17 + -3x

Combine like terms: -8x + -3x = -11x
-20 + -11x + 3x2 = 17 + 3x + -17 + -3x

Reorder the terms:
-20 + -11x + 3x2 = 17 + -17 + 3x + -3x

Combine like terms: 17 + -17 = 0
-20 + -11x + 3x2 = 0 + 3x + -3x
-20 + -11x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-20 + -11x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.333333333, 5}

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