(6x^2)-27x=(-3x^2)-5x-8

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Solution for (6x^2)-27x=(-3x^2)-5x-8 equation: 


Simplifying
(6x2) + -27x = (-3x2) + -5x + -8

Reorder the terms:
-27x + (6x2) = (-3x2) + -5x + -8

Reorder the terms:
-27x + (6x2) = -8 + -5x + (-3x2)

Solving
-27x + (6x2) = -8 + -5x + (-3x2)

Solving for variable 'x'.

Reorder the terms:
8 + -27x + 5x + (6x2) + (3x2) = -8 + -5x + (-3x2) + 8 + 5x + (3x2)

Combine like terms: -27x + 5x = -22x
8 + -22x + (6x2) + (3x2) = -8 + -5x + (-3x2) + 8 + 5x + (3x2)

Combine like terms: (6x2) + (3x2) = 9x2
8 + -22x + 9x2 = -8 + -5x + (-3x2) + 8 + 5x + (3x2)

Reorder the terms:
8 + -22x + 9x2 = -8 + 8 + -5x + 5x + (-3x2) + (3x2)

Combine like terms: -8 + 8 = 0
8 + -22x + 9x2 = 0 + -5x + 5x + (-3x2) + (3x2)
8 + -22x + 9x2 = -5x + 5x + (-3x2) + (3x2)

Combine like terms: -5x + 5x = 0
8 + -22x + 9x2 = 0 + (-3x2) + (3x2)
8 + -22x + 9x2 = (-3x2) + (3x2)

Combine like terms: (-3x2) + (3x2) = 0
8 + -22x + 9x2 = 0

Factor a trinomial.
(4 + -9x)(2 + -1x) = 0


Subproblem 1
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.4444444444, 2}

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