4(90x^2-x-1)=0

Solution for 4(90x^2-x-1)=0 equation:

Simplifying
4(90x2 + -1x + -1) = 0

Reorder the terms:
4(-1 + -1x + 90x2) = 0
(-1 * 4 + -1x * 4 + 90x2 * 4) = 0
(-4 + -4x + 360x2) = 0

Solving
-4 + -4x + 360x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -1x + 90x2) = 0

Factor a trinomial.
4((-1 + -10x)(1 + -9x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -10x)' equal to zero and attempt to solve:

Simplifying
-1 + -10x = 0

Solving
-1 + -10x = 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 + -10x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -10x = 0 + 1
-10x = 0 + 1

Combine like terms: 0 + 1 = 1
-10x = 1

Divide each side by '-10'.
x = -0.1

Simplifying
x = -0.1
Subproblem 2
Set the factor '(1 + -9x)' equal to zero and attempt to solve:

Simplifying
1 + -9x = 0

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

Combine like terms: 1 + -1 = 0
0 + -9x = 0 + -1
-9x = 0 + -1

Combine like terms: 0 + -1 = -1
-9x = -1

Divide each side by '-9'.
x = 0.1111111111

Simplifying
x = 0.1111111111
Solution
x = {-0.1, 0.1111111111}