x(3x+6)=(x+2)

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Solution for x(3x+6)=(x+2) equation:


Simplifying
x(3x + 6) = (x + 2)

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

Reorder the terms:
6x + 3x2 = (2 + x)

Remove parenthesis around (2 + x)
6x + 3x2 = 2 + x

Solving
6x + 3x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
-2 + 6x + -1x + 3x2 = 2 + x + -2 + -1x

Combine like terms: 6x + -1x = 5x
-2 + 5x + 3x2 = 2 + x + -2 + -1x

Reorder the terms:
-2 + 5x + 3x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
-2 + 5x + 3x2 = 0 + x + -1x
-2 + 5x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + 5x + 3x2 = 0

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

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

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 = {-2, 0.3333333333}

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