x(x+1(x+2(x+3)))=10

Solution for x(x+1(x+2(x+3)))=10 equation:

Simplifying
x(x + 1(x + 2(x + 3))) = 10

Reorder the terms:
x(x + 1(x + 2(3 + x))) = 10
x(x + 1(x + (3 * 2 + x * 2))) = 10
x(x + 1(x + (6 + 2x))) = 10

Reorder the terms:
x(x + 1(6 + x + 2x)) = 10

Combine like terms: x + 2x = 3x
x(x + 1(6 + 3x)) = 10
x(x + (6 * 1 + 3x * 1)) = 10
x(x + (6 + 3x)) = 10

Reorder the terms:
x(6 + x + 3x) = 10

Combine like terms: x + 3x = 4x
x(6 + 4x) = 10
(6 * x + 4x * x) = 10
(6x + 4x2) = 10

Solving
6x + 4x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 6x + 4x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 3x + 2x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.5, 1}