x(x+1)=7x

Solution for x(x+1)=7x equation:

Simplifying
x(x + 1) = 7x

Reorder the terms:
x(1 + x) = 7x
(1 * x + x * x) = 7x
(1x + x2) = 7x

Solving
1x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
1x + -7x + x2 = 7x + -7x

Combine like terms: 1x + -7x = -6x
-6x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-6x + x2 = 0

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