7x^3=42x^2

Solution for 7x^3=42x^2 equation:

Simplifying
7x3 = 42x2

Solving
7x3 = 42x2

Solving for variable 'x'.

Reorder the terms:
-42x2 + 7x3 = 42x2 + -42x2

Combine like terms: 42x2 + -42x2 = 0
-42x2 + 7x3 = 0

Factor out the Greatest Common Factor (GCF), '7x2'.
7x2(-6 + x) = 0

Ignore the factor 7.
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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}