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

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


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

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

Combine like terms: 1 + 2 = 3
3(3 + x + x + x) = (x + 1)(x + 2)

Combine like terms: x + x = 2x
3(3 + 2x + x) = (x + 1)(x + 2)

Combine like terms: 2x + x = 3x
3(3 + 3x) = (x + 1)(x + 2)
(3 * 3 + 3x * 3) = (x + 1)(x + 2)
(9 + 9x) = (x + 1)(x + 2)

Reorder the terms:
9 + 9x = (1 + x)(x + 2)

Reorder the terms:
9 + 9x = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
9 + 9x = (1(2 + x) + x(2 + x))
9 + 9x = ((2 * 1 + x * 1) + x(2 + x))
9 + 9x = ((2 + 1x) + x(2 + x))
9 + 9x = (2 + 1x + (2 * x + x * x))
9 + 9x = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
9 + 9x = (2 + 3x + x2)

Solving
9 + 9x = 2 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -2 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 9 + -2 = 7
7 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Combine like terms: 9x + -3x = 6x
7 + 6x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2

Reorder the terms:
7 + 6x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
7 + 6x + -1x2 = 0 + 3x + -3x + x2 + -1x2
7 + 6x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
7 + 6x + -1x2 = 0 + x2 + -1x2
7 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 6x + -1x2 = 0

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

Subproblem 1

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. 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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