3(x+1)(x+1)-(x+3)(2x+2)=0

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Solution for 3(x+1)(x+1)-(x+3)(2x+2)=0 equation:


Simplifying
3(x + 1)(x + 1) + -1(x + 3)(2x + 2) = 0

Reorder the terms:
3(1 + x)(x + 1) + -1(x + 3)(2x + 2) = 0

Reorder the terms:
3(1 + x)(1 + x) + -1(x + 3)(2x + 2) = 0

Multiply (1 + x) * (1 + x)
3(1(1 + x) + x(1 + x)) + -1(x + 3)(2x + 2) = 0
3((1 * 1 + x * 1) + x(1 + x)) + -1(x + 3)(2x + 2) = 0
3((1 + 1x) + x(1 + x)) + -1(x + 3)(2x + 2) = 0
3(1 + 1x + (1 * x + x * x)) + -1(x + 3)(2x + 2) = 0
3(1 + 1x + (1x + x2)) + -1(x + 3)(2x + 2) = 0

Combine like terms: 1x + 1x = 2x
3(1 + 2x + x2) + -1(x + 3)(2x + 2) = 0
(1 * 3 + 2x * 3 + x2 * 3) + -1(x + 3)(2x + 2) = 0
(3 + 6x + 3x2) + -1(x + 3)(2x + 2) = 0

Reorder the terms:
3 + 6x + 3x2 + -1(3 + x)(2x + 2) = 0

Reorder the terms:
3 + 6x + 3x2 + -1(3 + x)(2 + 2x) = 0

Multiply (3 + x) * (2 + 2x)
3 + 6x + 3x2 + -1(3(2 + 2x) + x(2 + 2x)) = 0
3 + 6x + 3x2 + -1((2 * 3 + 2x * 3) + x(2 + 2x)) = 0
3 + 6x + 3x2 + -1((6 + 6x) + x(2 + 2x)) = 0
3 + 6x + 3x2 + -1(6 + 6x + (2 * x + 2x * x)) = 0
3 + 6x + 3x2 + -1(6 + 6x + (2x + 2x2)) = 0

Combine like terms: 6x + 2x = 8x
3 + 6x + 3x2 + -1(6 + 8x + 2x2) = 0
3 + 6x + 3x2 + (6 * -1 + 8x * -1 + 2x2 * -1) = 0
3 + 6x + 3x2 + (-6 + -8x + -2x2) = 0

Reorder the terms:
3 + -6 + 6x + -8x + 3x2 + -2x2 = 0

Combine like terms: 3 + -6 = -3
-3 + 6x + -8x + 3x2 + -2x2 = 0

Combine like terms: 6x + -8x = -2x
-3 + -2x + 3x2 + -2x2 = 0

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

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

Solving for variable 'x'.

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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