4x^2+12x+9=x^2-6x+9

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Solution for 4x^2+12x+9=x^2-6x+9 equation: 


Simplifying
4x2 + 12x + 9 = x2 + -6x + 9

Reorder the terms:
9 + 12x + 4x2 = x2 + -6x + 9

Reorder the terms:
9 + 12x + 4x2 = 9 + -6x + x2

Add '-9' to each side of the equation.
9 + 12x + -9 + 4x2 = 9 + -6x + -9 + x2

Reorder the terms:
9 + -9 + 12x + 4x2 = 9 + -6x + -9 + x2

Combine like terms: 9 + -9 = 0
0 + 12x + 4x2 = 9 + -6x + -9 + x2
12x + 4x2 = 9 + -6x + -9 + x2

Reorder the terms:
12x + 4x2 = 9 + -9 + -6x + x2

Combine like terms: 9 + -9 = 0
12x + 4x2 = 0 + -6x + x2
12x + 4x2 = -6x + x2

Solving
12x + 4x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
12x + 6x + 4x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 12x + 6x = 18x
18x + 4x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
18x + 3x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
18x + 3x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
18x + 3x2 = 0 + x2 + -1x2
18x + 3x2 = x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), '3x'.
3x(6 + x) = 0

Ignore the factor 3.

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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0, -6}

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