(x+2)(3x+5)=(2x)(x+9)

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Solution for (x+2)(3x+5)=(2x)(x+9) equation: 


Simplifying
(x + 2)(3x + 5) = (2x)(x + 9)

Reorder the terms:
(2 + x)(3x + 5) = (2x)(x + 9)

Reorder the terms:
(2 + x)(5 + 3x) = (2x)(x + 9)

Multiply (2 + x) * (5 + 3x)
(2(5 + 3x) + x(5 + 3x)) = (2x)(x + 9)
((5 * 2 + 3x * 2) + x(5 + 3x)) = (2x)(x + 9)
((10 + 6x) + x(5 + 3x)) = (2x)(x + 9)
(10 + 6x + (5 * x + 3x * x)) = (2x)(x + 9)
(10 + 6x + (5x + 3x2)) = (2x)(x + 9)

Combine like terms: 6x + 5x = 11x
(10 + 11x + 3x2) = (2x)(x + 9)

Remove parenthesis around (2x)
10 + 11x + 3x2 = 2x(x + 9)

Reorder the terms:
10 + 11x + 3x2 = 2x(9 + x)
10 + 11x + 3x2 = (9 * 2x + x * 2x)
10 + 11x + 3x2 = (18x + 2x2)

Solving
10 + 11x + 3x2 = 18x + 2x2

Solving for variable 'x'.

Reorder the terms:
10 + 11x + -18x + 3x2 + -2x2 = 18x + 2x2 + -18x + -2x2

Combine like terms: 11x + -18x = -7x
10 + -7x + 3x2 + -2x2 = 18x + 2x2 + -18x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
10 + -7x + 1x2 = 18x + 2x2 + -18x + -2x2

Reorder the terms:
10 + -7x + 1x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
10 + -7x + 1x2 = 0 + 2x2 + -2x2
10 + -7x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + -7x + 1x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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