(3x+1)(9x^2-3x+1)=x^2(27x+4)

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Solution for (3x+1)(9x^2-3x+1)=x^2(27x+4) equation: 


Simplifying
(3x + 1)(9x2 + -3x + 1) = x2(27x + 4)

Reorder the terms:
(1 + 3x)(9x2 + -3x + 1) = x2(27x + 4)

Reorder the terms:
(1 + 3x)(1 + -3x + 9x2) = x2(27x + 4)

Multiply (1 + 3x) * (1 + -3x + 9x2)
(1(1 + -3x + 9x2) + 3x * (1 + -3x + 9x2)) = x2(27x + 4)
((1 * 1 + -3x * 1 + 9x2 * 1) + 3x * (1 + -3x + 9x2)) = x2(27x + 4)
((1 + -3x + 9x2) + 3x * (1 + -3x + 9x2)) = x2(27x + 4)
(1 + -3x + 9x2 + (1 * 3x + -3x * 3x + 9x2 * 3x)) = x2(27x + 4)
(1 + -3x + 9x2 + (3x + -9x2 + 27x3)) = x2(27x + 4)

Reorder the terms:
(1 + -3x + 3x + 9x2 + -9x2 + 27x3) = x2(27x + 4)

Combine like terms: -3x + 3x = 0
(1 + 0 + 9x2 + -9x2 + 27x3) = x2(27x + 4)
(1 + 9x2 + -9x2 + 27x3) = x2(27x + 4)

Combine like terms: 9x2 + -9x2 = 0
(1 + 0 + 27x3) = x2(27x + 4)
(1 + 27x3) = x2(27x + 4)

Reorder the terms:
1 + 27x3 = x2(4 + 27x)
1 + 27x3 = (4 * x2 + 27x * x2)
1 + 27x3 = (4x2 + 27x3)

Add '-27x3' to each side of the equation.
1 + 27x3 + -27x3 = 4x2 + 27x3 + -27x3

Combine like terms: 27x3 + -27x3 = 0
1 + 0 = 4x2 + 27x3 + -27x3
1 = 4x2 + 27x3 + -27x3

Combine like terms: 27x3 + -27x3 = 0
1 = 4x2 + 0
1 = 4x2

Solving
1 = 4x2

Solving for variable 'x'.

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

Add '-4x2' to each side of the equation.
1 + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
1 + -4x2 = 0

Add '-1' to each side of the equation.
1 + -1 + -4x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x2 = 0 + -1
-4x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x2 = -1

Divide each side by '-4'.
x2 = 0.25

Simplifying
x2 = 0.25

Take the square root of each side:
x = {-0.5, 0.5}

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