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

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


Simplifying
0 = (4x + -1)(9x + -2)

Reorder the terms:
0 = (-1 + 4x)(9x + -2)

Reorder the terms:
0 = (-1 + 4x)(-2 + 9x)

Multiply (-1 + 4x) * (-2 + 9x)
0 = (-1(-2 + 9x) + 4x * (-2 + 9x))
0 = ((-2 * -1 + 9x * -1) + 4x * (-2 + 9x))
0 = ((2 + -9x) + 4x * (-2 + 9x))
0 = (2 + -9x + (-2 * 4x + 9x * 4x))
0 = (2 + -9x + (-8x + 36x2))

Combine like terms: -9x + -8x = -17x
0 = (2 + -17x + 36x2)

Solving
0 = 2 + -17x + 36x2

Solving for variable 'x'.

Combine like terms: 0 + -2 = -2
-2 + 17x + -36x2 = 2 + -17x + 36x2 + -2 + 17x + -36x2

Reorder the terms:
-2 + 17x + -36x2 = 2 + -2 + -17x + 17x + 36x2 + -36x2

Combine like terms: 2 + -2 = 0
-2 + 17x + -36x2 = 0 + -17x + 17x + 36x2 + -36x2
-2 + 17x + -36x2 = -17x + 17x + 36x2 + -36x2

Combine like terms: -17x + 17x = 0
-2 + 17x + -36x2 = 0 + 36x2 + -36x2
-2 + 17x + -36x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
-2 + 17x + -36x2 = 0

Factor a trinomial.
(-1 + 4x)(2 + -9x) = 0


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

Simplifying
-1 + 4x = 0

Solving
-1 + 4x = 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 + 4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x = 0 + 1
4x = 0 + 1

Combine like terms: 0 + 1 = 1
4x = 1

Divide each side by '4'.
x = 0.25

Simplifying
x = 0.25

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

Simplifying
2 + -9x = 0

Solving
2 + -9x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x = 0 + -2
-9x = 0 + -2

Combine like terms: 0 + -2 = -2
-9x = -2

Divide each side by '-9'.
x = 0.2222222222

Simplifying
x = 0.2222222222
Solution
x = {0.25, 0.2222222222}

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