x^2-6-10x+15=3x-3

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Solution for x^2-6-10x+15=3x-3 equation: 


Simplifying
x2 + -6 + -10x + 15 = 3x + -3

Reorder the terms:
-6 + 15 + -10x + x2 = 3x + -3

Combine like terms: -6 + 15 = 9
9 + -10x + x2 = 3x + -3

Reorder the terms:
9 + -10x + x2 = -3 + 3x

Solving
9 + -10x + x2 = -3 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + 3 + -10x + -3x + x2 = -3 + 3x + 3 + -3x

Combine like terms: 9 + 3 = 12
12 + -10x + -3x + x2 = -3 + 3x + 3 + -3x

Combine like terms: -10x + -3x = -13x
12 + -13x + x2 = -3 + 3x + 3 + -3x

Reorder the terms:
12 + -13x + x2 = -3 + 3 + 3x + -3x

Combine like terms: -3 + 3 = 0
12 + -13x + x2 = 0 + 3x + -3x
12 + -13x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -13x + x2 = 0

Factor a trinomial.
(1 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {1, 12}

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