x*x-8x+20=10x-12

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Solution for x*x-8x+20=10x-12 equation: 


Simplifying
x * x + -8x + 20 = 10x + -12

Multiply x * x
x2 + -8x + 20 = 10x + -12

Reorder the terms:
20 + -8x + x2 = 10x + -12

Reorder the terms:
20 + -8x + x2 = -12 + 10x

Solving
20 + -8x + x2 = -12 + 10x

Solving for variable 'x'.

Reorder the terms:
20 + 12 + -8x + -10x + x2 = -12 + 10x + 12 + -10x

Combine like terms: 20 + 12 = 32
32 + -8x + -10x + x2 = -12 + 10x + 12 + -10x

Combine like terms: -8x + -10x = -18x
32 + -18x + x2 = -12 + 10x + 12 + -10x

Reorder the terms:
32 + -18x + x2 = -12 + 12 + 10x + -10x

Combine like terms: -12 + 12 = 0
32 + -18x + x2 = 0 + 10x + -10x
32 + -18x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
32 + -18x + x2 = 0

Factor a trinomial.
(2 + -1x)(16 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {2, 16}

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