(x+2)(2x)=(x+1)(x+1)+2

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


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

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

Remove parenthesis around (2x)
(2 + x) * 2x = (x + 1)(x + 1) + 2

Reorder the terms for easier multiplication:
2x(2 + x) = (x + 1)(x + 1) + 2
(2 * 2x + x * 2x) = (x + 1)(x + 1) + 2
(4x + 2x2) = (x + 1)(x + 1) + 2

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

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

Multiply (1 + x) * (1 + x)
4x + 2x2 = (1(1 + x) + x(1 + x)) + 2
4x + 2x2 = ((1 * 1 + x * 1) + x(1 + x)) + 2
4x + 2x2 = ((1 + 1x) + x(1 + x)) + 2
4x + 2x2 = (1 + 1x + (1 * x + x * x)) + 2
4x + 2x2 = (1 + 1x + (1x + x2)) + 2

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

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

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

Solving
4x + 2x2 = 3 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 4x + -2x + 2x2 + -1x2 = 3 + 2x + x2 + -3 + -2x + -1x2

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

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

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

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

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

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

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

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

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, 1}

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