x^2(4x-3)(5x-1)=0

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Solution for x^2(4x-3)(5x-1)=0 equation: 


Simplifying
x2(4x + -3)(5x + -1) = 0

Reorder the terms:
x2(-3 + 4x)(5x + -1) = 0

Reorder the terms:
x2(-3 + 4x)(-1 + 5x) = 0

Multiply (-3 + 4x) * (-1 + 5x)
x2(-3(-1 + 5x) + 4x * (-1 + 5x)) = 0
x2((-1 * -3 + 5x * -3) + 4x * (-1 + 5x)) = 0
x2((3 + -15x) + 4x * (-1 + 5x)) = 0
x2(3 + -15x + (-1 * 4x + 5x * 4x)) = 0
x2(3 + -15x + (-4x + 20x2)) = 0

Combine like terms: -15x + -4x = -19x
x2(3 + -19x + 20x2) = 0
(3 * x2 + -19x * x2 + 20x2 * x2) = 0
(3x2 + -19x3 + 20x4) = 0

Solving
3x2 + -19x3 + 20x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3 + -19x + 20x2) = 0

Factor a trinomial.
x2((1 + -5x)(3 + -4x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

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

Simplifying
3 + -4x = 0

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

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, 0.2, 0.75}

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