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

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

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

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

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

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

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

Reorder the terms:
1 + 2x + 3x + x2 = 7

Combine like terms: 2x + 3x = 5x
1 + 5x + x2 = 7

Solving
1 + 5x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 5x + x2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 5x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + 5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 1}