2(x+9)=3x+2(x^2-9)

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


Simplifying
2(x + 9) = 3x + 2(x2 + -9)

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

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

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

Solving
18 + 2x = -18 + 3x + 2x2

Solving for variable 'x'.

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

Combine like terms: 18 + 18 = 36
36 + 2x + -3x + -2x2 = -18 + 3x + 2x2 + 18 + -3x + -2x2

Combine like terms: 2x + -3x = -1x
36 + -1x + -2x2 = -18 + 3x + 2x2 + 18 + -3x + -2x2

Reorder the terms:
36 + -1x + -2x2 = -18 + 18 + 3x + -3x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
36 + -1x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
36 + -1x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
36 + -1x + -2x2 = 0 + 2x2 + -2x2
36 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
36 + -1x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(9 + 2x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
9 + 2x = 0

Solving
9 + 2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {4, -4.5}

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