(2x+1)(1+x)=2(1-x)+6

Solution for (2x+1)(1+x)=2(1-x)+6 equation:

Simplifying
(2x + 1)(1 + x) = 2(1 + -1x) + 6

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

Multiply (1 + 2x) * (1 + x)
(1(1 + x) + 2x * (1 + x)) = 2(1 + -1x) + 6
((1 * 1 + x * 1) + 2x * (1 + x)) = 2(1 + -1x) + 6
((1 + 1x) + 2x * (1 + x)) = 2(1 + -1x) + 6
(1 + 1x + (1 * 2x + x * 2x)) = 2(1 + -1x) + 6
(1 + 1x + (2x + 2x2)) = 2(1 + -1x) + 6

Combine like terms: 1x + 2x = 3x
(1 + 3x + 2x2) = 2(1 + -1x) + 6
1 + 3x + 2x2 = (1 * 2 + -1x * 2) + 6
1 + 3x + 2x2 = (2 + -2x) + 6

Reorder the terms:
1 + 3x + 2x2 = 2 + 6 + -2x

Combine like terms: 2 + 6 = 8
1 + 3x + 2x2 = 8 + -2x

Solving
1 + 3x + 2x2 = 8 + -2x

Solving for variable 'x'.

Reorder the terms:
1 + -8 + 3x + 2x + 2x2 = 8 + -2x + -8 + 2x

Combine like terms: 1 + -8 = -7
-7 + 3x + 2x + 2x2 = 8 + -2x + -8 + 2x

Combine like terms: 3x + 2x = 5x
-7 + 5x + 2x2 = 8 + -2x + -8 + 2x

Reorder the terms:
-7 + 5x + 2x2 = 8 + -8 + -2x + 2x

Combine like terms: 8 + -8 = 0
-7 + 5x + 2x2 = 0 + -2x + 2x
-7 + 5x + 2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-7 + 5x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5
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 = {-3.5, 1}