x(3x-1)=6x(x-2)-20

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Solution for x(3x-1)=6x(x-2)-20 equation: 


Simplifying
x(3x + -1) = 6x(x + -2) + -20

Reorder the terms:
x(-1 + 3x) = 6x(x + -2) + -20
(-1 * x + 3x * x) = 6x(x + -2) + -20
(-1x + 3x2) = 6x(x + -2) + -20

Reorder the terms:
-1x + 3x2 = 6x(-2 + x) + -20
-1x + 3x2 = (-2 * 6x + x * 6x) + -20
-1x + 3x2 = (-12x + 6x2) + -20

Reorder the terms:
-1x + 3x2 = -20 + -12x + 6x2

Solving
-1x + 3x2 = -20 + -12x + 6x2

Solving for variable 'x'.

Reorder the terms:
20 + -1x + 12x + 3x2 + -6x2 = -20 + -12x + 6x2 + 20 + 12x + -6x2

Combine like terms: -1x + 12x = 11x
20 + 11x + 3x2 + -6x2 = -20 + -12x + 6x2 + 20 + 12x + -6x2

Combine like terms: 3x2 + -6x2 = -3x2
20 + 11x + -3x2 = -20 + -12x + 6x2 + 20 + 12x + -6x2

Reorder the terms:
20 + 11x + -3x2 = -20 + 20 + -12x + 12x + 6x2 + -6x2

Combine like terms: -20 + 20 = 0
20 + 11x + -3x2 = 0 + -12x + 12x + 6x2 + -6x2
20 + 11x + -3x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
20 + 11x + -3x2 = 0 + 6x2 + -6x2
20 + 11x + -3x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
20 + 11x + -3x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {5, -1.333333333}

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