(2*x^2+9*x+12)=(3*x^2+8*x+12)

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Solution for (2*x^2+9*x+12)=(3*x^2+8*x+12) equation: 


Simplifying
(2x2 + 9x + 12) = (3x2 + 8x + 12)

Reorder the terms:
(12 + 9x + 2x2) = (3x2 + 8x + 12)

Remove parenthesis around (12 + 9x + 2x2)
12 + 9x + 2x2 = (3x2 + 8x + 12)

Reorder the terms:
12 + 9x + 2x2 = (12 + 8x + 3x2)

Remove parenthesis around (12 + 8x + 3x2)
12 + 9x + 2x2 = 12 + 8x + 3x2

Add '-12' to each side of the equation.
12 + 9x + -12 + 2x2 = 12 + 8x + -12 + 3x2

Reorder the terms:
12 + -12 + 9x + 2x2 = 12 + 8x + -12 + 3x2

Combine like terms: 12 + -12 = 0
0 + 9x + 2x2 = 12 + 8x + -12 + 3x2
9x + 2x2 = 12 + 8x + -12 + 3x2

Reorder the terms:
9x + 2x2 = 12 + -12 + 8x + 3x2

Combine like terms: 12 + -12 = 0
9x + 2x2 = 0 + 8x + 3x2
9x + 2x2 = 8x + 3x2

Solving
9x + 2x2 = 8x + 3x2

Solving for variable 'x'.

Reorder the terms:
9x + -8x + 2x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: 9x + -8x = 1x
1x + 2x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
1x + -1x2 = 8x + 3x2 + -8x + -3x2

Reorder the terms:
1x + -1x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
1x + -1x2 = 0 + 3x2 + -3x2
1x + -1x2 = 3x2 + -3x2

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, 1}

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