x^2(x-7)(4x-1)=0

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Solution for x^2(x-7)(4x-1)=0 equation: 


Simplifying
x2(x + -7)(4x + -1) = 0

Reorder the terms:
x2(-7 + x)(4x + -1) = 0

Reorder the terms:
x2(-7 + x)(-1 + 4x) = 0

Multiply (-7 + x) * (-1 + 4x)
x2(-7(-1 + 4x) + x(-1 + 4x)) = 0
x2((-1 * -7 + 4x * -7) + x(-1 + 4x)) = 0
x2((7 + -28x) + x(-1 + 4x)) = 0
x2(7 + -28x + (-1 * x + 4x * x)) = 0
x2(7 + -28x + (-1x + 4x2)) = 0

Combine like terms: -28x + -1x = -29x
x2(7 + -29x + 4x2) = 0
(7 * x2 + -29x * x2 + 4x2 * x2) = 0
(7x2 + -29x3 + 4x4) = 0

Solving
7x2 + -29x3 + 4x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(7 + -29x + 4x2) = 0

Factor a trinomial.
x2((1 + -4x)(7 + -1x)) = 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 + -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 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

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

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

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 0.25, 7}

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