2(x+1)(x+1)+7(x+1)+3=

Solution for 2(x+1)(x+1)+7(x+1)+3= equation:

Simplifying
2(x + 1)(x + 1) + 7(x + 1) + 3 = 0

Reorder the terms:
2(1 + x)(x + 1) + 7(x + 1) + 3 = 0

Reorder the terms:
2(1 + x)(1 + x) + 7(x + 1) + 3 = 0

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) + 7(x + 1) + 3 = 0
2((1 * 1 + x * 1) + x(1 + x)) + 7(x + 1) + 3 = 0
2((1 + 1x) + x(1 + x)) + 7(x + 1) + 3 = 0
2(1 + 1x + (1 * x + x * x)) + 7(x + 1) + 3 = 0
2(1 + 1x + (1x + x2)) + 7(x + 1) + 3 = 0

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) + 7(x + 1) + 3 = 0
(1 * 2 + 2x * 2 + x2 * 2) + 7(x + 1) + 3 = 0
(2 + 4x + 2x2) + 7(x + 1) + 3 = 0

Reorder the terms:
2 + 4x + 2x2 + 7(1 + x) + 3 = 0
2 + 4x + 2x2 + (1 * 7 + x * 7) + 3 = 0
2 + 4x + 2x2 + (7 + 7x) + 3 = 0

Reorder the terms:
2 + 7 + 3 + 4x + 7x + 2x2 = 0

Combine like terms: 2 + 7 = 9
9 + 3 + 4x + 7x + 2x2 = 0

Combine like terms: 9 + 3 = 12
12 + 4x + 7x + 2x2 = 0

Combine like terms: 4x + 7x = 11x
12 + 11x + 2x2 = 0

Solving
12 + 11x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(3 + 2x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-4, -1.5}