(x+3)(3x-1)=12x-4x^2

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Solution for (x+3)(3x-1)=12x-4x^2 equation: 


Simplifying
(x + 3)(3x + -1) = 12x + -4x2

Reorder the terms:
(3 + x)(3x + -1) = 12x + -4x2

Reorder the terms:
(3 + x)(-1 + 3x) = 12x + -4x2

Multiply (3 + x) * (-1 + 3x)
(3(-1 + 3x) + x(-1 + 3x)) = 12x + -4x2
((-1 * 3 + 3x * 3) + x(-1 + 3x)) = 12x + -4x2
((-3 + 9x) + x(-1 + 3x)) = 12x + -4x2
(-3 + 9x + (-1 * x + 3x * x)) = 12x + -4x2
(-3 + 9x + (-1x + 3x2)) = 12x + -4x2

Combine like terms: 9x + -1x = 8x
(-3 + 8x + 3x2) = 12x + -4x2

Solving
-3 + 8x + 3x2 = 12x + -4x2

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + -12x + 3x2 + 4x2 = 12x + -4x2 + -12x + 4x2

Combine like terms: 8x + -12x = -4x
-3 + -4x + 3x2 + 4x2 = 12x + -4x2 + -12x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
-3 + -4x + 7x2 = 12x + -4x2 + -12x + 4x2

Reorder the terms:
-3 + -4x + 7x2 = 12x + -12x + -4x2 + 4x2

Combine like terms: 12x + -12x = 0
-3 + -4x + 7x2 = 0 + -4x2 + 4x2
-3 + -4x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-3 + -4x + 7x2 = 0

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


Subproblem 1
Set the factor '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.4285714286, 1}

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