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

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


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

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

Multiply (3 + x) * (3 + -2x)
9 + -1x2 = (3(3 + -2x) + x(3 + -2x))
9 + -1x2 = ((3 * 3 + -2x * 3) + x(3 + -2x))
9 + -1x2 = ((9 + -6x) + x(3 + -2x))
9 + -1x2 = (9 + -6x + (3 * x + -2x * x))
9 + -1x2 = (9 + -6x + (3x + -2x2))

Combine like terms: -6x + 3x = -3x
9 + -1x2 = (9 + -3x + -2x2)

Add '-9' to each side of the equation.
9 + -9 + -1x2 = 9 + -3x + -9 + -2x2

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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
Solution
x = {0, -3}

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