3x(x+1)=4-8x

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Solution for 3x(x+1)=4-8x equation: 


Simplifying
3x(x + 1) = 4 + -8x

Reorder the terms:
3x(1 + x) = 4 + -8x
(1 * 3x + x * 3x) = 4 + -8x
(3x + 3x2) = 4 + -8x

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

Solving for variable 'x'.

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

Combine like terms: 3x + 8x = 11x
-4 + 11x + 3x2 = 4 + -8x + -4 + 8x

Reorder the terms:
-4 + 11x + 3x2 = 4 + -4 + -8x + 8x

Combine like terms: 4 + -4 = 0
-4 + 11x + 3x2 = 0 + -8x + 8x
-4 + 11x + 3x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-4 + 11x + 3x2 = 0

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


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 0.3333333333}

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