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

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


Simplifying
4x2 + 12x + 9 = 2x2 + -6x + 9

Reorder the terms:
9 + 12x + 4x2 = 2x2 + -6x + 9

Reorder the terms:
9 + 12x + 4x2 = 9 + -6x + 2x2

Add '-9' to each side of the equation.
9 + 12x + -9 + 4x2 = 9 + -6x + -9 + 2x2

Reorder the terms:
9 + -9 + 12x + 4x2 = 9 + -6x + -9 + 2x2

Combine like terms: 9 + -9 = 0
0 + 12x + 4x2 = 9 + -6x + -9 + 2x2
12x + 4x2 = 9 + -6x + -9 + 2x2

Reorder the terms:
12x + 4x2 = 9 + -9 + -6x + 2x2

Combine like terms: 9 + -9 = 0
12x + 4x2 = 0 + -6x + 2x2
12x + 4x2 = -6x + 2x2

Solving
12x + 4x2 = -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
12x + 6x + 4x2 + -2x2 = -6x + 2x2 + 6x + -2x2

Combine like terms: 12x + 6x = 18x
18x + 4x2 + -2x2 = -6x + 2x2 + 6x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
18x + 2x2 = -6x + 2x2 + 6x + -2x2

Reorder the terms:
18x + 2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
18x + 2x2 = 0 + 2x2 + -2x2
18x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {0, -9}

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