(4x^2-1)-(18x^2-9x)=0

Solution for (4x^2-1)-(18x^2-9x)=0 equation:

Simplifying
(4x2 + -1) + -1(18x2 + -9x) = 0

Reorder the terms:
(-1 + 4x2) + -1(18x2 + -9x) = 0

Remove parenthesis around (-1 + 4x2)
-1 + 4x2 + -1(18x2 + -9x) = 0

Reorder the terms:
-1 + 4x2 + -1(-9x + 18x2) = 0
-1 + 4x2 + (-9x * -1 + 18x2 * -1) = 0
-1 + 4x2 + (9x + -18x2) = 0

Reorder the terms:
-1 + 9x + 4x2 + -18x2 = 0

Combine like terms: 4x2 + -18x2 = -14x2
-1 + 9x + -14x2 = 0

Solving
-1 + 9x + -14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + 2x)(1 + -7x) = 0

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

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x = 0 + 1
2x = 0 + 1

Combine like terms: 0 + 1 = 1
2x = 1

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {0.5, 0.1428571429}