6x(x+1)=20-x

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


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

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

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

Solving for variable 'x'.

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

Combine like terms: 6x + x = 7x
-20 + 7x + 6x2 = 20 + -1x + -20 + x

Reorder the terms:
-20 + 7x + 6x2 = 20 + -20 + -1x + x

Combine like terms: 20 + -20 = 0
-20 + 7x + 6x2 = 0 + -1x + x
-20 + 7x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-20 + 7x + 6x2 = 0

Factor a trinomial.
(-5 + -2x)(4 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 1.333333333}

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