2(3x-1)+(5-x)(3x-1)=0

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Solution for 2(3x-1)+(5-x)(3x-1)=0 equation: 


Simplifying
2(3x + -1) + (5 + -1x)(3x + -1) = 0

Reorder the terms:
2(-1 + 3x) + (5 + -1x)(3x + -1) = 0
(-1 * 2 + 3x * 2) + (5 + -1x)(3x + -1) = 0
(-2 + 6x) + (5 + -1x)(3x + -1) = 0

Reorder the terms:
-2 + 6x + (5 + -1x)(-1 + 3x) = 0

Multiply (5 + -1x) * (-1 + 3x)
-2 + 6x + (5(-1 + 3x) + -1x * (-1 + 3x)) = 0
-2 + 6x + ((-1 * 5 + 3x * 5) + -1x * (-1 + 3x)) = 0
-2 + 6x + ((-5 + 15x) + -1x * (-1 + 3x)) = 0
-2 + 6x + (-5 + 15x + (-1 * -1x + 3x * -1x)) = 0
-2 + 6x + (-5 + 15x + (1x + -3x2)) = 0

Combine like terms: 15x + 1x = 16x
-2 + 6x + (-5 + 16x + -3x2) = 0

Reorder the terms:
-2 + -5 + 6x + 16x + -3x2 = 0

Combine like terms: -2 + -5 = -7
-7 + 6x + 16x + -3x2 = 0

Combine like terms: 6x + 16x = 22x
-7 + 22x + -3x2 = 0

Solving
-7 + 22x + -3x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

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

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

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

Simplifying
x = 7

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 = {7, 0.3333333333}

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