20x^2=x(42+x)

Solution for 20x^2=x(42+x) equation:

Simplifying
20x2 = x(42 + x)
20x2 = (42 * x + x * x)
20x2 = (42x + x2)

Solving
20x2 = 42x + x2

Solving for variable 'x'.

Reorder the terms:
-42x + 20x2 + -1x2 = 42x + x2 + -42x + -1x2

Combine like terms: 20x2 + -1x2 = 19x2
-42x + 19x2 = 42x + x2 + -42x + -1x2

Reorder the terms:
-42x + 19x2 = 42x + -42x + x2 + -1x2

Combine like terms: 42x + -42x = 0
-42x + 19x2 = 0 + x2 + -1x2
-42x + 19x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42x + 19x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-42 + 19x) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-42 + 19x)' equal to zero and attempt to solve:

Simplifying
-42 + 19x = 0

Solving
-42 + 19x = 0

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

Add '42' to each side of the equation.
-42 + 42 + 19x = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 19x = 0 + 42
19x = 0 + 42

Combine like terms: 0 + 42 = 42
19x = 42

Divide each side by '19'.
x = 2.210526316

Simplifying
x = 2.210526316
Solution
x = {0, 2.210526316}