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

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


Simplifying
6x + -1x2 = 9 + 4x2 + -12x

Reorder the terms:
6x + -1x2 = 9 + -12x + 4x2

Solving
6x + -1x2 = 9 + -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
-9 + 6x + 12x + -1x2 + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: 6x + 12x = 18x
-9 + 18x + -1x2 + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Combine like terms: -1x2 + -4x2 = -5x2
-9 + 18x + -5x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2

Reorder the terms:
-9 + 18x + -5x2 = 9 + -9 + -12x + 12x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
-9 + 18x + -5x2 = 0 + -12x + 12x + 4x2 + -4x2
-9 + 18x + -5x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
-9 + 18x + -5x2 = 0 + 4x2 + -4x2
-9 + 18x + -5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-9 + 18x + -5x2 = 0

Factor a trinomial.
(-3 + x)(3 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {3, 0.6}

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