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

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


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

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

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

Solving
15 + -10x + x2 = -15 + 3x

Solving for variable 'x'.

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

Combine like terms: 15 + 15 = 30
30 + -10x + -3x + x2 = -15 + 3x + 15 + -3x

Combine like terms: -10x + -3x = -13x
30 + -13x + x2 = -15 + 3x + 15 + -3x

Reorder the terms:
30 + -13x + x2 = -15 + 15 + 3x + -3x

Combine like terms: -15 + 15 = 0
30 + -13x + x2 = 0 + 3x + -3x
30 + -13x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
30 + -13x + x2 = 0

Factor a trinomial.
(3 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}

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