15x+45=27x^2-5x+45-3x

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Solution for 15x+45=27x^2-5x+45-3x equation: 


Simplifying
15x + 45 = 27x2 + -5x + 45 + -3x

Reorder the terms:
45 + 15x = 27x2 + -5x + 45 + -3x

Reorder the terms:
45 + 15x = 45 + -5x + -3x + 27x2

Combine like terms: -5x + -3x = -8x
45 + 15x = 45 + -8x + 27x2

Add '-45' to each side of the equation.
45 + -45 + 15x = 45 + -8x + -45 + 27x2

Combine like terms: 45 + -45 = 0
0 + 15x = 45 + -8x + -45 + 27x2
15x = 45 + -8x + -45 + 27x2

Reorder the terms:
15x = 45 + -45 + -8x + 27x2

Combine like terms: 45 + -45 = 0
15x = 0 + -8x + 27x2
15x = -8x + 27x2

Solving
15x = -8x + 27x2

Solving for variable 'x'.

Combine like terms: 15x + 8x = 23x
23x + -27x2 = -8x + 27x2 + 8x + -27x2

Reorder the terms:
23x + -27x2 = -8x + 8x + 27x2 + -27x2

Combine like terms: -8x + 8x = 0
23x + -27x2 = 0 + 27x2 + -27x2
23x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
23x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(23 + -27x) = 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 '(23 + -27x)' equal to zero and attempt to solve:

Simplifying
23 + -27x = 0

Solving
23 + -27x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -27x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -27x = 0 + -23
-27x = 0 + -23

Combine like terms: 0 + -23 = -23
-27x = -23

Divide each side by '-27'.
x = 0.8518518519

Simplifying
x = 0.8518518519
Solution
x = {0, 0.8518518519}

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