(x+1)(x+1)-4x(x+1)=0

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Solution for (x+1)(x+1)-4x(x+1)=0 equation: 


Simplifying
(x + 1)(x + 1) + -4x(x + 1) = 0

Reorder the terms:
(1 + x)(x + 1) + -4x(x + 1) = 0

Reorder the terms:
(1 + x)(1 + x) + -4x(x + 1) = 0

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -4x(x + 1) = 0
((1 * 1 + x * 1) + x(1 + x)) + -4x(x + 1) = 0
((1 + 1x) + x(1 + x)) + -4x(x + 1) = 0
(1 + 1x + (1 * x + x * x)) + -4x(x + 1) = 0
(1 + 1x + (1x + x2)) + -4x(x + 1) = 0

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -4x(x + 1) = 0

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

Reorder the terms:
1 + 2x + -4x + x2 + -4x2 = 0

Combine like terms: 2x + -4x = -2x
1 + -2x + x2 + -4x2 = 0

Combine like terms: x2 + -4x2 = -3x2
1 + -2x + -3x2 = 0

Solving
1 + -2x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(1 + x) = 0


Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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 = {0.3333333333, -1}

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