(x+1)(x+1)=2x^2+10x+8

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Solution for (x+1)(x+1)=2x^2+10x+8 equation: 


Simplifying
(x + 1)(x + 1) = 2x2 + 10x + 8

Reorder the terms:
(1 + x)(x + 1) = 2x2 + 10x + 8

Reorder the terms:
(1 + x)(1 + x) = 2x2 + 10x + 8

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 2x2 + 10x + 8
((1 * 1 + x * 1) + x(1 + x)) = 2x2 + 10x + 8
((1 + 1x) + x(1 + x)) = 2x2 + 10x + 8
(1 + 1x + (1 * x + x * x)) = 2x2 + 10x + 8
(1 + 1x + (1x + x2)) = 2x2 + 10x + 8

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 2x2 + 10x + 8

Reorder the terms:
1 + 2x + x2 = 8 + 10x + 2x2

Solving
1 + 2x + x2 = 8 + 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + -8 + 2x + -10x + x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 1 + -8 = -7
-7 + 2x + -10x + x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 2x + -10x = -8x
-7 + -8x + x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-7 + -8x + -1x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Reorder the terms:
-7 + -8x + -1x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-7 + -8x + -1x2 = 0 + 10x + -10x + 2x2 + -2x2
-7 + -8x + -1x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-7 + -8x + -1x2 = 0 + 2x2 + -2x2
-7 + -8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-7 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8x + x2) = 0

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

Ignore the factor -1.

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

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-7, -1}

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