(9x^2+8)(6)-(6x-1)(18x+8)=0

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Solution for (9x^2+8)(6)-(6x-1)(18x+8)=0 equation: 


Simplifying
(9x2 + 8)(6) + -1(6x + -1)(18x + 8) = 0

Reorder the terms:
(8 + 9x2)(6) + -1(6x + -1)(18x + 8) = 0

Reorder the terms for easier multiplication:
6(8 + 9x2) + -1(6x + -1)(18x + 8) = 0
(8 * 6 + 9x2 * 6) + -1(6x + -1)(18x + 8) = 0
(48 + 54x2) + -1(6x + -1)(18x + 8) = 0

Reorder the terms:
48 + 54x2 + -1(-1 + 6x)(18x + 8) = 0

Reorder the terms:
48 + 54x2 + -1(-1 + 6x)(8 + 18x) = 0

Multiply (-1 + 6x) * (8 + 18x)
48 + 54x2 + -1(-1(8 + 18x) + 6x * (8 + 18x)) = 0
48 + 54x2 + -1((8 * -1 + 18x * -1) + 6x * (8 + 18x)) = 0
48 + 54x2 + -1((-8 + -18x) + 6x * (8 + 18x)) = 0
48 + 54x2 + -1(-8 + -18x + (8 * 6x + 18x * 6x)) = 0
48 + 54x2 + -1(-8 + -18x + (48x + 108x2)) = 0

Combine like terms: -18x + 48x = 30x
48 + 54x2 + -1(-8 + 30x + 108x2) = 0
48 + 54x2 + (-8 * -1 + 30x * -1 + 108x2 * -1) = 0
48 + 54x2 + (8 + -30x + -108x2) = 0

Reorder the terms:
48 + 8 + -30x + 54x2 + -108x2 = 0

Combine like terms: 48 + 8 = 56
56 + -30x + 54x2 + -108x2 = 0

Combine like terms: 54x2 + -108x2 = -54x2
56 + -30x + -54x2 = 0

Solving
56 + -30x + -54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -15x + -27x2) = 0

Factor a trinomial.
2((7 + -9x)(4 + 3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -9x)' equal to zero and attempt to solve:

Simplifying
7 + -9x = 0

Solving
7 + -9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9x = 0 + -7
-9x = 0 + -7

Combine like terms: 0 + -7 = -7
-9x = -7

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {0.7777777778, -1.333333333}

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