81(1-4x)=3(x^2-10x+12)

Solution for 81(1-4x)=3(x^2-10x+12) equation:

Simplifying
81(1 + -4x) = 3(x2 + -10x + 12)
(1 * 81 + -4x * 81) = 3(x2 + -10x + 12)
(81 + -324x) = 3(x2 + -10x + 12)

Reorder the terms:
81 + -324x = 3(12 + -10x + x2)
81 + -324x = (12 * 3 + -10x * 3 + x2 * 3)
81 + -324x = (36 + -30x + 3x2)

Solving
81 + -324x = 36 + -30x + 3x2

Solving for variable 'x'.

Reorder the terms:
81 + -36 + -324x + 30x + -3x2 = 36 + -30x + 3x2 + -36 + 30x + -3x2

Combine like terms: 81 + -36 = 45
45 + -324x + 30x + -3x2 = 36 + -30x + 3x2 + -36 + 30x + -3x2

Combine like terms: -324x + 30x = -294x
45 + -294x + -3x2 = 36 + -30x + 3x2 + -36 + 30x + -3x2

Reorder the terms:
45 + -294x + -3x2 = 36 + -36 + -30x + 30x + 3x2 + -3x2

Combine like terms: 36 + -36 = 0
45 + -294x + -3x2 = 0 + -30x + 30x + 3x2 + -3x2
45 + -294x + -3x2 = -30x + 30x + 3x2 + -3x2

Combine like terms: -30x + 30x = 0
45 + -294x + -3x2 = 0 + 3x2 + -3x2
45 + -294x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
45 + -294x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -98x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(15 + -98x + -1x2)' equal to zero and attempt to solve:

Simplifying
15 + -98x + -1x2 = 0

Solving
15 + -98x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15 + 98x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 98x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 98x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 98x + x2 = 0 + 15
98x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
98x + x2 = 15

The x term is 98x.  Take half its coefficient (49).
Square it (2401) and add it to both sides.

Add '2401' to each side of the equation.
98x + 2401 + x2 = 15 + 2401

Reorder the terms:
2401 + 98x + x2 = 15 + 2401

Combine like terms: 15 + 2401 = 2416
2401 + 98x + x2 = 2416

Factor a perfect square on the left side:
(x + 49)(x + 49) = 2416

Calculate the square root of the right side: 49.15282291

Break this problem into two subproblems by setting 
(x + 49) equal to 49.15282291 and -49.15282291.

Subproblem 1
x + 49 = 49.15282291

Simplifying
x + 49 = 49.15282291

Reorder the terms:
49 + x = 49.15282291

Solving
49 + x = 49.15282291

Solving for variable 'x'.

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

Add '-49' to each side of the equation.
49 + -49 + x = 49.15282291 + -49

Combine like terms: 49 + -49 = 0
0 + x = 49.15282291 + -49
x = 49.15282291 + -49

Combine like terms: 49.15282291 + -49 = 0.15282291
x = 0.15282291

Simplifying
x = 0.15282291

Subproblem 2
x + 49 = -49.15282291

Simplifying
x + 49 = -49.15282291

Reorder the terms:
49 + x = -49.15282291

Solving
49 + x = -49.15282291

Solving for variable 'x'.

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

Add '-49' to each side of the equation.
49 + -49 + x = -49.15282291 + -49

Combine like terms: 49 + -49 = 0
0 + x = -49.15282291 + -49
x = -49.15282291 + -49

Combine like terms: -49.15282291 + -49 = -98.15282291
x = -98.15282291

Simplifying
x = -98.15282291

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15282291, -98.15282291}
Solution
x = {0.15282291, -98.15282291}