(x+1)(x+2)=12-6(x^2-1x)

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Solution for (x+1)(x+2)=12-6(x^2-1x) equation: 


Simplifying
(x + 1)(x + 2) = 12 + -6(x2 + -1x)

Reorder the terms:
(1 + x)(x + 2) = 12 + -6(x2 + -1x)

Reorder the terms:
(1 + x)(2 + x) = 12 + -6(x2 + -1x)

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 12 + -6(x2 + -1x)
((2 * 1 + x * 1) + x(2 + x)) = 12 + -6(x2 + -1x)
((2 + 1x) + x(2 + x)) = 12 + -6(x2 + -1x)
(2 + 1x + (2 * x + x * x)) = 12 + -6(x2 + -1x)
(2 + 1x + (2x + x2)) = 12 + -6(x2 + -1x)

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 12 + -6(x2 + -1x)

Reorder the terms:
2 + 3x + x2 = 12 + -6(-1x + x2)
2 + 3x + x2 = 12 + (-1x * -6 + x2 * -6)
2 + 3x + x2 = 12 + (6x + -6x2)

Solving
2 + 3x + x2 = 12 + 6x + -6x2

Solving for variable 'x'.

Reorder the terms:
2 + -12 + 3x + -6x + x2 + 6x2 = 12 + 6x + -6x2 + -12 + -6x + 6x2

Combine like terms: 2 + -12 = -10
-10 + 3x + -6x + x2 + 6x2 = 12 + 6x + -6x2 + -12 + -6x + 6x2

Combine like terms: 3x + -6x = -3x
-10 + -3x + x2 + 6x2 = 12 + 6x + -6x2 + -12 + -6x + 6x2

Combine like terms: x2 + 6x2 = 7x2
-10 + -3x + 7x2 = 12 + 6x + -6x2 + -12 + -6x + 6x2

Reorder the terms:
-10 + -3x + 7x2 = 12 + -12 + 6x + -6x + -6x2 + 6x2

Combine like terms: 12 + -12 = 0
-10 + -3x + 7x2 = 0 + 6x + -6x + -6x2 + 6x2
-10 + -3x + 7x2 = 6x + -6x + -6x2 + 6x2

Combine like terms: 6x + -6x = 0
-10 + -3x + 7x2 = 0 + -6x2 + 6x2
-10 + -3x + 7x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-10 + -3x + 7x2 = 0

Factor a trinomial.
(-1 + -1x)(10 + -7x) = 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 '(10 + -7x)' equal to zero and attempt to solve:

Simplifying
10 + -7x = 0

Solving
10 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7x = 0 + -10
-7x = 0 + -10

Combine like terms: 0 + -10 = -10
-7x = -10

Divide each side by '-7'.
x = 1.428571429

Simplifying
x = 1.428571429
Solution
x = {-1, 1.428571429}

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