6x(x+1)=x+4

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Solution for 6x(x+1)=x+4 equation: 


Simplifying
6x(x + 1) = x + 4

Reorder the terms:
6x(1 + x) = x + 4
(1 * 6x + x * 6x) = x + 4
(6x + 6x2) = x + 4

Reorder the terms:
6x + 6x2 = 4 + x

Solving
6x + 6x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-4 + 6x + -1x + 6x2 = 4 + x + -4 + -1x

Combine like terms: 6x + -1x = 5x
-4 + 5x + 6x2 = 4 + x + -4 + -1x

Reorder the terms:
-4 + 5x + 6x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-4 + 5x + 6x2 = 0 + x + -1x
-4 + 5x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + 5x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(1 + -2x) = 0


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.333333333, 0.5}

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