(3x+1)*(x-3)=4*(3-x)

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Solution for (3x+1)*(x-3)=4*(3-x) equation:


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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -3 + -12 = -15
-15 + -8x + 4x + 3x2 = 12 + -4x + -12 + 4x

Combine like terms: -8x + 4x = -4x
-15 + -4x + 3x2 = 12 + -4x + -12 + 4x

Reorder the terms:
-15 + -4x + 3x2 = 12 + -12 + -4x + 4x

Combine like terms: 12 + -12 = 0
-15 + -4x + 3x2 = 0 + -4x + 4x
-15 + -4x + 3x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-15 + -4x + 3x2 = 0

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


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.666666667, 3}

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