9(x+1)(x+1)=(x+2)(x+2)

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Solution for 9(x+1)(x+1)=(x+2)(x+2) equation: 


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

Reorder the terms:
9(1 + x)(x + 1) = (x + 2)(x + 2)

Reorder the terms:
9(1 + x)(1 + x) = (x + 2)(x + 2)

Multiply (1 + x) * (1 + x)
9(1(1 + x) + x(1 + x)) = (x + 2)(x + 2)
9((1 * 1 + x * 1) + x(1 + x)) = (x + 2)(x + 2)
9((1 + 1x) + x(1 + x)) = (x + 2)(x + 2)
9(1 + 1x + (1 * x + x * x)) = (x + 2)(x + 2)
9(1 + 1x + (1x + x2)) = (x + 2)(x + 2)

Combine like terms: 1x + 1x = 2x
9(1 + 2x + x2) = (x + 2)(x + 2)
(1 * 9 + 2x * 9 + x2 * 9) = (x + 2)(x + 2)
(9 + 18x + 9x2) = (x + 2)(x + 2)

Reorder the terms:
9 + 18x + 9x2 = (2 + x)(x + 2)

Reorder the terms:
9 + 18x + 9x2 = (2 + x)(2 + x)

Multiply (2 + x) * (2 + x)
9 + 18x + 9x2 = (2(2 + x) + x(2 + x))
9 + 18x + 9x2 = ((2 * 2 + x * 2) + x(2 + x))
9 + 18x + 9x2 = ((4 + 2x) + x(2 + x))
9 + 18x + 9x2 = (4 + 2x + (2 * x + x * x))
9 + 18x + 9x2 = (4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
9 + 18x + 9x2 = (4 + 4x + x2)

Solving
9 + 18x + 9x2 = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -4 + 18x + -4x + 9x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 9 + -4 = 5
5 + 18x + -4x + 9x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 18x + -4x = 14x
5 + 14x + 9x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
5 + 14x + 8x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
5 + 14x + 8x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
5 + 14x + 8x2 = 0 + 4x + -4x + x2 + -1x2
5 + 14x + 8x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
5 + 14x + 8x2 = 0 + x2 + -1x2
5 + 14x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 14x + 8x2 = 0

Factor a trinomial.
(5 + 4x)(1 + 2x) = 0


Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.25, -0.5}

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