(4x-1)(5x-2)-16x^2+1=0

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Solution for (4x-1)(5x-2)-16x^2+1=0 equation: 


Simplifying
(4x + -1)(5x + -2) + -16x2 + 1 = 0

Reorder the terms:
(-1 + 4x)(5x + -2) + -16x2 + 1 = 0

Reorder the terms:
(-1 + 4x)(-2 + 5x) + -16x2 + 1 = 0

Multiply (-1 + 4x) * (-2 + 5x)
(-1(-2 + 5x) + 4x * (-2 + 5x)) + -16x2 + 1 = 0
((-2 * -1 + 5x * -1) + 4x * (-2 + 5x)) + -16x2 + 1 = 0
((2 + -5x) + 4x * (-2 + 5x)) + -16x2 + 1 = 0
(2 + -5x + (-2 * 4x + 5x * 4x)) + -16x2 + 1 = 0
(2 + -5x + (-8x + 20x2)) + -16x2 + 1 = 0

Combine like terms: -5x + -8x = -13x
(2 + -13x + 20x2) + -16x2 + 1 = 0

Reorder the terms:
2 + 1 + -13x + 20x2 + -16x2 = 0

Combine like terms: 2 + 1 = 3
3 + -13x + 20x2 + -16x2 = 0

Combine like terms: 20x2 + -16x2 = 4x2
3 + -13x + 4x2 = 0

Solving
3 + -13x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.25, 3}

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