36x-9x^2-18x+27=24x^2+48x+24

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Solution for 36x-9x^2-18x+27=24x^2+48x+24 equation: 


Simplifying
36x + -9x2 + -18x + 27 = 24x2 + 48x + 24

Reorder the terms:
27 + 36x + -18x + -9x2 = 24x2 + 48x + 24

Combine like terms: 36x + -18x = 18x
27 + 18x + -9x2 = 24x2 + 48x + 24

Reorder the terms:
27 + 18x + -9x2 = 24 + 48x + 24x2

Solving
27 + 18x + -9x2 = 24 + 48x + 24x2

Solving for variable 'x'.

Reorder the terms:
27 + -24 + 18x + -48x + -9x2 + -24x2 = 24 + 48x + 24x2 + -24 + -48x + -24x2

Combine like terms: 27 + -24 = 3
3 + 18x + -48x + -9x2 + -24x2 = 24 + 48x + 24x2 + -24 + -48x + -24x2

Combine like terms: 18x + -48x = -30x
3 + -30x + -9x2 + -24x2 = 24 + 48x + 24x2 + -24 + -48x + -24x2

Combine like terms: -9x2 + -24x2 = -33x2
3 + -30x + -33x2 = 24 + 48x + 24x2 + -24 + -48x + -24x2

Reorder the terms:
3 + -30x + -33x2 = 24 + -24 + 48x + -48x + 24x2 + -24x2

Combine like terms: 24 + -24 = 0
3 + -30x + -33x2 = 0 + 48x + -48x + 24x2 + -24x2
3 + -30x + -33x2 = 48x + -48x + 24x2 + -24x2

Combine like terms: 48x + -48x = 0
3 + -30x + -33x2 = 0 + 24x2 + -24x2
3 + -30x + -33x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
3 + -30x + -33x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -10x + -11x2) = 0

Factor a trinomial.
3((1 + -11x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -11x)' equal to zero and attempt to solve:

Simplifying
1 + -11x = 0

Solving
1 + -11x = 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 + -11x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -11x = 0 + -1
-11x = 0 + -1

Combine like terms: 0 + -1 = -1
-11x = -1

Divide each side by '-11'.
x = 0.09090909091

Simplifying
x = 0.09090909091

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0.09090909091, -1}

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