(x-3)(x+3)=3x(x+1)+3x-9

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Solution for (x-3)(x+3)=3x(x+1)+3x-9 equation:


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

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

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

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

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

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

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

Combine like terms: 3x + 3x = 6x
-9 + x2 = -9 + 6x + 3x2

Add '9' to each side of the equation.
-9 + 9 + x2 = -9 + 6x + 9 + 3x2

Combine like terms: -9 + 9 = 0
0 + x2 = -9 + 6x + 9 + 3x2
x2 = -9 + 6x + 9 + 3x2

Reorder the terms:
x2 = -9 + 9 + 6x + 3x2

Combine like terms: -9 + 9 = 0
x2 = 0 + 6x + 3x2
x2 = 6x + 3x2

Solving
x2 = 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6x + x2 + -3x2 = 6x + 3x2 + -6x + -3x2

Combine like terms: x2 + -3x2 = -2x2
-6x + -2x2 = 6x + 3x2 + -6x + -3x2

Reorder the terms:
-6x + -2x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-6x + -2x2 = 0 + 3x2 + -3x2
-6x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(3 + x) = 0

Ignore the factor -2.

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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