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

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


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

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

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

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

Multiply (-3 + x) * (6 + x)
12x + 2x2 = (-3(6 + x) + x(6 + x))
12x + 2x2 = ((6 * -3 + x * -3) + x(6 + x))
12x + 2x2 = ((-18 + -3x) + x(6 + x))
12x + 2x2 = (-18 + -3x + (6 * x + x * x))
12x + 2x2 = (-18 + -3x + (6x + x2))

Combine like terms: -3x + 6x = 3x
12x + 2x2 = (-18 + 3x + x2)

Solving
12x + 2x2 = -18 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
18 + 12x + -3x + 2x2 + -1x2 = -18 + 3x + x2 + 18 + -3x + -1x2

Combine like terms: 12x + -3x = 9x
18 + 9x + 2x2 + -1x2 = -18 + 3x + x2 + 18 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
18 + 9x + 1x2 = -18 + 3x + x2 + 18 + -3x + -1x2

Reorder the terms:
18 + 9x + 1x2 = -18 + 18 + 3x + -3x + x2 + -1x2

Combine like terms: -18 + 18 = 0
18 + 9x + 1x2 = 0 + 3x + -3x + x2 + -1x2
18 + 9x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
18 + 9x + 1x2 = 0 + x2 + -1x2
18 + 9x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
18 + 9x + 1x2 = 0

Factor a trinomial.
(6 + x)(3 + x) = 0


Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-6, -3}

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