40[x+(x+2)]=9[x(x+2)]

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Solution for 40[x+(x+2)]=9[x(x+2)] equation: 


Simplifying
40[x + (x + 2)] = 9[x(x + 2)]

Reorder the terms:
40[x + (2 + x)] = 9[x(x + 2)]

Remove parenthesis around (2 + x)
40[x + 2 + x] = 9[x(x + 2)]

Reorder the terms:
40[2 + x + x] = 9[x(x + 2)]

Combine like terms: x + x = 2x
40[2 + 2x] = 9[x(x + 2)]
[2 * 40 + 2x * 40] = 9[x(x + 2)]
[80 + 80x] = 9[x(x + 2)]

Reorder the terms:
80 + 80x = 9[x(2 + x)]
80 + 80x = 9[(2 * x + x * x)]
80 + 80x = 9[(2x + x2)]
80 + 80x = [2x * 9 + x2 * 9]
80 + 80x = [18x + 9x2]

Solving
80 + 80x = 18x + 9x2

Solving for variable 'x'.

Combine like terms: 80x + -18x = 62x
80 + 62x + -9x2 = 18x + 9x2 + -18x + -9x2

Reorder the terms:
80 + 62x + -9x2 = 18x + -18x + 9x2 + -9x2

Combine like terms: 18x + -18x = 0
80 + 62x + -9x2 = 0 + 9x2 + -9x2
80 + 62x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
80 + 62x + -9x2 = 0

Factor a trinomial.
(8 + -1x)(10 + 9x) = 0


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(10 + 9x)' equal to zero and attempt to solve:

Simplifying
10 + 9x = 0

Solving
10 + 9x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 9x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9x = 0 + -10
9x = 0 + -10

Combine like terms: 0 + -10 = -10
9x = -10

Divide each side by '9'.
x = -1.111111111

Simplifying
x = -1.111111111
Solution
x = {8, -1.111111111}

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