2x(x-2)+3(x+4)=x(x-5)+9

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Solution for 2x(x-2)+3(x+4)=x(x-5)+9 equation: 


Simplifying
2x(x + -2) + 3(x + 4) = x(x + -5) + 9

Reorder the terms:
2x(-2 + x) + 3(x + 4) = x(x + -5) + 9
(-2 * 2x + x * 2x) + 3(x + 4) = x(x + -5) + 9
(-4x + 2x2) + 3(x + 4) = x(x + -5) + 9

Reorder the terms:
-4x + 2x2 + 3(4 + x) = x(x + -5) + 9
-4x + 2x2 + (4 * 3 + x * 3) = x(x + -5) + 9
-4x + 2x2 + (12 + 3x) = x(x + -5) + 9

Reorder the terms:
12 + -4x + 3x + 2x2 = x(x + -5) + 9

Combine like terms: -4x + 3x = -1x
12 + -1x + 2x2 = x(x + -5) + 9

Reorder the terms:
12 + -1x + 2x2 = x(-5 + x) + 9
12 + -1x + 2x2 = (-5 * x + x * x) + 9
12 + -1x + 2x2 = (-5x + x2) + 9

Reorder the terms:
12 + -1x + 2x2 = 9 + -5x + x2

Solving
12 + -1x + 2x2 = 9 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -9 + -1x + 5x + 2x2 + -1x2 = 9 + -5x + x2 + -9 + 5x + -1x2

Combine like terms: 12 + -9 = 3
3 + -1x + 5x + 2x2 + -1x2 = 9 + -5x + x2 + -9 + 5x + -1x2

Combine like terms: -1x + 5x = 4x
3 + 4x + 2x2 + -1x2 = 9 + -5x + x2 + -9 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
3 + 4x + 1x2 = 9 + -5x + x2 + -9 + 5x + -1x2

Reorder the terms:
3 + 4x + 1x2 = 9 + -9 + -5x + 5x + x2 + -1x2

Combine like terms: 9 + -9 = 0
3 + 4x + 1x2 = 0 + -5x + 5x + x2 + -1x2
3 + 4x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
3 + 4x + 1x2 = 0 + x2 + -1x2
3 + 4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x + 1x2 = 0

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


Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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 = {-3, -1}

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