x^2+2x+1=4x+4

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Solution for x^2+2x+1=4x+4 equation:


Simplifying
x2 + 2x + 1 = 4x + 4

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

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

Solving
1 + 2x + x2 = 4 + 4x

Solving for variable 'x'.

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

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

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

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

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

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

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-1, 3}

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