8(x+1)=(x+9)(x+1)

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Solution for 8(x+1)=(x+9)(x+1) equation:


Simplifying
8(x + 1) = (x + 9)(x + 1)

Reorder the terms:
8(1 + x) = (x + 9)(x + 1)
(1 * 8 + x * 8) = (x + 9)(x + 1)
(8 + 8x) = (x + 9)(x + 1)

Reorder the terms:
8 + 8x = (9 + x)(x + 1)

Reorder the terms:
8 + 8x = (9 + x)(1 + x)

Multiply (9 + x) * (1 + x)
8 + 8x = (9(1 + x) + x(1 + x))
8 + 8x = ((1 * 9 + x * 9) + x(1 + x))
8 + 8x = ((9 + 9x) + x(1 + x))
8 + 8x = (9 + 9x + (1 * x + x * x))
8 + 8x = (9 + 9x + (1x + x2))

Combine like terms: 9x + 1x = 10x
8 + 8x = (9 + 10x + x2)

Solving
8 + 8x = 9 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
8 + -9 + 8x + -10x + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Combine like terms: 8 + -9 = -1
-1 + 8x + -10x + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Combine like terms: 8x + -10x = -2x
-1 + -2x + -1x2 = 9 + 10x + x2 + -9 + -10x + -1x2

Reorder the terms:
-1 + -2x + -1x2 = 9 + -9 + 10x + -10x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-1 + -2x + -1x2 = 0 + 10x + -10x + x2 + -1x2
-1 + -2x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-1 + -2x + -1x2 = 0 + x2 + -1x2
-1 + -2x + -1x2 = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x + x2) = 0

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

Ignore the factor -1.

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1

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

Simplifying
1 + x = 0

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

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

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

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

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