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

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


Simplifying
-1x2 + 2x + 3 = x2 + -3x + -9

Reorder the terms:
3 + 2x + -1x2 = x2 + -3x + -9

Reorder the terms:
3 + 2x + -1x2 = -9 + -3x + x2

Solving
3 + 2x + -1x2 = -9 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
3 + 9 + 2x + 3x + -1x2 + -1x2 = -9 + -3x + x2 + 9 + 3x + -1x2

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

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

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

Reorder the terms:
12 + 5x + -2x2 = -9 + 9 + -3x + 3x + x2 + -1x2

Combine like terms: -9 + 9 = 0
12 + 5x + -2x2 = 0 + -3x + 3x + x2 + -1x2
12 + 5x + -2x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
12 + 5x + -2x2 = 0 + x2 + -1x2
12 + 5x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 5x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(3 + 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 '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {4, -1.5}

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