12x+12-x^2+1=15x-15

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Solution for 12x+12-x^2+1=15x-15 equation: 


Simplifying
12x + 12 + -1x2 + 1 = 15x + -15

Reorder the terms:
12 + 1 + 12x + -1x2 = 15x + -15

Combine like terms: 12 + 1 = 13
13 + 12x + -1x2 = 15x + -15

Reorder the terms:
13 + 12x + -1x2 = -15 + 15x

Solving
13 + 12x + -1x2 = -15 + 15x

Solving for variable 'x'.

Reorder the terms:
13 + 15 + 12x + -15x + -1x2 = -15 + 15x + 15 + -15x

Combine like terms: 13 + 15 = 28
28 + 12x + -15x + -1x2 = -15 + 15x + 15 + -15x

Combine like terms: 12x + -15x = -3x
28 + -3x + -1x2 = -15 + 15x + 15 + -15x

Reorder the terms:
28 + -3x + -1x2 = -15 + 15 + 15x + -15x

Combine like terms: -15 + 15 = 0
28 + -3x + -1x2 = 0 + 15x + -15x
28 + -3x + -1x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
28 + -3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(7 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {4, -7}

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