2x(x+6)=(x+1)(x+6)

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Solution for 2x(x+6)=(x+1)(x+6) equation: 


Simplifying
2x(x + 6) = (x + 1)(x + 6)

Reorder the terms:
2x(6 + x) = (x + 1)(x + 6)
(6 * 2x + x * 2x) = (x + 1)(x + 6)
(12x + 2x2) = (x + 1)(x + 6)

Reorder the terms:
12x + 2x2 = (1 + x)(x + 6)

Reorder the terms:
12x + 2x2 = (1 + x)(6 + x)

Multiply (1 + x) * (6 + x)
12x + 2x2 = (1(6 + x) + x(6 + x))
12x + 2x2 = ((6 * 1 + x * 1) + x(6 + x))
12x + 2x2 = ((6 + 1x) + x(6 + x))
12x + 2x2 = (6 + 1x + (6 * x + x * x))
12x + 2x2 = (6 + 1x + (6x + x2))

Combine like terms: 1x + 6x = 7x
12x + 2x2 = (6 + 7x + x2)

Solving
12x + 2x2 = 6 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + -7x + 2x2 + -1x2 = 6 + 7x + x2 + -6 + -7x + -1x2

Combine like terms: 12x + -7x = 5x
-6 + 5x + 2x2 + -1x2 = 6 + 7x + x2 + -6 + -7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-6 + 5x + 1x2 = 6 + 7x + x2 + -6 + -7x + -1x2

Reorder the terms:
-6 + 5x + 1x2 = 6 + -6 + 7x + -7x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-6 + 5x + 1x2 = 0 + 7x + -7x + x2 + -1x2
-6 + 5x + 1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-6 + 5x + 1x2 = 0 + x2 + -1x2
-6 + 5x + 1x2 = x2 + -1x2

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

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0


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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-6, 1}

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