(28x^3-49x^2)(-24x+42)=0

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Solution for (28x^3-49x^2)(-24x+42)=0 equation: 


Simplifying
(28x3 + -49x2)(-24x + 42) = 0

Reorder the terms:
(-49x2 + 28x3)(-24x + 42) = 0

Reorder the terms:
(-49x2 + 28x3)(42 + -24x) = 0

Multiply (-49x2 + 28x3) * (42 + -24x)
(-49x2 * (42 + -24x) + 28x3 * (42 + -24x)) = 0
((42 * -49x2 + -24x * -49x2) + 28x3 * (42 + -24x)) = 0
((-2058x2 + 1176x3) + 28x3 * (42 + -24x)) = 0
(-2058x2 + 1176x3 + (42 * 28x3 + -24x * 28x3)) = 0
(-2058x2 + 1176x3 + (1176x3 + -672x4)) = 0

Combine like terms: 1176x3 + 1176x3 = 2352x3
(-2058x2 + 2352x3 + -672x4) = 0

Solving
-2058x2 + 2352x3 + -672x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '42x2'.
42x2(-49 + 56x + -16x2) = 0

Factor a trinomial.
42x2((-7 + 4x)(7 + -4x)) = 0

Ignore the factor 42.

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 '(-7 + 4x)' equal to zero and attempt to solve:

Simplifying
-7 + 4x = 0

Solving
-7 + 4x = 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 + 4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 0 + 7
4x = 0 + 7

Combine like terms: 0 + 7 = 7
4x = 7

Divide each side by '4'.
x = 1.75

Simplifying
x = 1.75

Subproblem 3
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {0, 1.75, 1.75}

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