3x^2-27x=-4x^2-3x-9

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Solution for 3x^2-27x=-4x^2-3x-9 equation: 


Simplifying
3x2 + -27x = -4x2 + -3x + -9

Reorder the terms:
-27x + 3x2 = -4x2 + -3x + -9

Reorder the terms:
-27x + 3x2 = -9 + -3x + -4x2

Solving
-27x + 3x2 = -9 + -3x + -4x2

Solving for variable 'x'.

Reorder the terms:
9 + -27x + 3x + 3x2 + 4x2 = -9 + -3x + -4x2 + 9 + 3x + 4x2

Combine like terms: -27x + 3x = -24x
9 + -24x + 3x2 + 4x2 = -9 + -3x + -4x2 + 9 + 3x + 4x2

Combine like terms: 3x2 + 4x2 = 7x2
9 + -24x + 7x2 = -9 + -3x + -4x2 + 9 + 3x + 4x2

Reorder the terms:
9 + -24x + 7x2 = -9 + 9 + -3x + 3x + -4x2 + 4x2

Combine like terms: -9 + 9 = 0
9 + -24x + 7x2 = 0 + -3x + 3x + -4x2 + 4x2
9 + -24x + 7x2 = -3x + 3x + -4x2 + 4x2

Combine like terms: -3x + 3x = 0
9 + -24x + 7x2 = 0 + -4x2 + 4x2
9 + -24x + 7x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
9 + -24x + 7x2 = 0

Factor a trinomial.
(3 + -7x)(3 + -1x) = 0


Subproblem 1
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.4285714286, 3}

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