x^2+(x+1)(x+2)=154

Solution for x^2+(x+1)(x+2)=154 equation:

Simplifying
x2 + (x + 1)(x + 2) = 154

Reorder the terms:
x2 + (1 + x)(x + 2) = 154

Reorder the terms:
x2 + (1 + x)(2 + x) = 154

Multiply (1 + x) * (2 + x)
x2 + (1(2 + x) + x(2 + x)) = 154
x2 + ((2 * 1 + x * 1) + x(2 + x)) = 154
x2 + ((2 + 1x) + x(2 + x)) = 154
x2 + (2 + 1x + (2 * x + x * x)) = 154
x2 + (2 + 1x + (2x + x2)) = 154

Combine like terms: 1x + 2x = 3x
x2 + (2 + 3x + x2) = 154

Reorder the terms:
2 + 3x + x2 + x2 = 154

Combine like terms: x2 + x2 = 2x2
2 + 3x + 2x2 = 154

Solving
2 + 3x + 2x2 = 154

Solving for variable 'x'.

Reorder the terms:
2 + -154 + 3x + 2x2 = 154 + -154

Combine like terms: 2 + -154 = -152
-152 + 3x + 2x2 = 154 + -154

Combine like terms: 154 + -154 = 0
-152 + 3x + 2x2 = 0

Factor a trinomial.
(-19 + -2x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-19 + -2x)' equal to zero and attempt to solve:

Simplifying
-19 + -2x = 0

Solving
-19 + -2x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2x = 0 + 19
-2x = 0 + 19

Combine like terms: 0 + 19 = 19
-2x = 19

Divide each side by '-2'.
x = -9.5

Simplifying
x = -9.5
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-9.5, 8}