6(9x^2-6x+1)+4=14(3x-1)

Solution for 6(9x^2-6x+1)+4=14(3x-1) equation:

Simplifying
6(9x2 + -6x + 1) + 4 = 14(3x + -1)

Reorder the terms:
6(1 + -6x + 9x2) + 4 = 14(3x + -1)
(1 * 6 + -6x * 6 + 9x2 * 6) + 4 = 14(3x + -1)
(6 + -36x + 54x2) + 4 = 14(3x + -1)

Reorder the terms:
6 + 4 + -36x + 54x2 = 14(3x + -1)

Combine like terms: 6 + 4 = 10
10 + -36x + 54x2 = 14(3x + -1)

Reorder the terms:
10 + -36x + 54x2 = 14(-1 + 3x)
10 + -36x + 54x2 = (-1 * 14 + 3x * 14)
10 + -36x + 54x2 = (-14 + 42x)

Solving
10 + -36x + 54x2 = -14 + 42x

Solving for variable 'x'.

Reorder the terms:
10 + 14 + -36x + -42x + 54x2 = -14 + 42x + 14 + -42x

Combine like terms: 10 + 14 = 24
24 + -36x + -42x + 54x2 = -14 + 42x + 14 + -42x

Combine like terms: -36x + -42x = -78x
24 + -78x + 54x2 = -14 + 42x + 14 + -42x

Reorder the terms:
24 + -78x + 54x2 = -14 + 14 + 42x + -42x

Combine like terms: -14 + 14 = 0
24 + -78x + 54x2 = 0 + 42x + -42x
24 + -78x + 54x2 = 42x + -42x

Combine like terms: 42x + -42x = 0
24 + -78x + 54x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -13x + 9x2) = 0

Factor a trinomial.
6((4 + -9x)(1 + -1x)) = 0

Ignore the factor 6.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0.4444444444, 1}