4x+10=x(x+1)

Solution for 4x+10=x(x+1) equation:

Simplifying
4x + 10 = x(x + 1)

Reorder the terms:
10 + 4x = x(x + 1)

Reorder the terms:
10 + 4x = x(1 + x)
10 + 4x = (1 * x + x * x)
10 + 4x = (1x + x2)

Solving
10 + 4x = 1x + x2

Solving for variable 'x'.

Combine like terms: 4x + -1x = 3x
10 + 3x + -1x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
10 + 3x + -1x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
10 + 3x + -1x2 = 0 + x2 + -1x2
10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 3x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {5, -2}