(3x-1)(x+3)+(3x-1)(-2x+12)=0

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Solution for (3x-1)(x+3)+(3x-1)(-2x+12)=0 equation: 


Simplifying
(3x + -1)(x + 3) + (3x + -1)(-2x + 12) = 0

Reorder the terms:
(-1 + 3x)(x + 3) + (3x + -1)(-2x + 12) = 0

Reorder the terms:
(-1 + 3x)(3 + x) + (3x + -1)(-2x + 12) = 0

Multiply (-1 + 3x) * (3 + x)
(-1(3 + x) + 3x * (3 + x)) + (3x + -1)(-2x + 12) = 0
((3 * -1 + x * -1) + 3x * (3 + x)) + (3x + -1)(-2x + 12) = 0
((-3 + -1x) + 3x * (3 + x)) + (3x + -1)(-2x + 12) = 0
(-3 + -1x + (3 * 3x + x * 3x)) + (3x + -1)(-2x + 12) = 0
(-3 + -1x + (9x + 3x2)) + (3x + -1)(-2x + 12) = 0

Combine like terms: -1x + 9x = 8x
(-3 + 8x + 3x2) + (3x + -1)(-2x + 12) = 0

Reorder the terms:
-3 + 8x + 3x2 + (-1 + 3x)(-2x + 12) = 0

Reorder the terms:
-3 + 8x + 3x2 + (-1 + 3x)(12 + -2x) = 0

Multiply (-1 + 3x) * (12 + -2x)
-3 + 8x + 3x2 + (-1(12 + -2x) + 3x * (12 + -2x)) = 0
-3 + 8x + 3x2 + ((12 * -1 + -2x * -1) + 3x * (12 + -2x)) = 0
-3 + 8x + 3x2 + ((-12 + 2x) + 3x * (12 + -2x)) = 0
-3 + 8x + 3x2 + (-12 + 2x + (12 * 3x + -2x * 3x)) = 0
-3 + 8x + 3x2 + (-12 + 2x + (36x + -6x2)) = 0

Combine like terms: 2x + 36x = 38x
-3 + 8x + 3x2 + (-12 + 38x + -6x2) = 0

Reorder the terms:
-3 + -12 + 8x + 38x + 3x2 + -6x2 = 0

Combine like terms: -3 + -12 = -15
-15 + 8x + 38x + 3x2 + -6x2 = 0

Combine like terms: 8x + 38x = 46x
-15 + 46x + 3x2 + -6x2 = 0

Combine like terms: 3x2 + -6x2 = -3x2
-15 + 46x + -3x2 = 0

Solving
-15 + 46x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-15 + x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-15 + x)' equal to zero and attempt to solve:

Simplifying
-15 + x = 0

Solving
-15 + x = 0

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

Add '15' to each side of the equation.
-15 + 15 + x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + x = 0 + 15
x = 0 + 15

Combine like terms: 0 + 15 = 15
x = 15

Simplifying
x = 15

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 = {15, 0.3333333333}

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