x^2-3x=7x-16

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Solution for x^2-3x=7x-16 equation: 


Simplifying
x2 + -3x = 7x + -16

Reorder the terms:
-3x + x2 = 7x + -16

Reorder the terms:
-3x + x2 = -16 + 7x

Solving
-3x + x2 = -16 + 7x

Solving for variable 'x'.

Reorder the terms:
16 + -3x + -7x + x2 = -16 + 7x + 16 + -7x

Combine like terms: -3x + -7x = -10x
16 + -10x + x2 = -16 + 7x + 16 + -7x

Reorder the terms:
16 + -10x + x2 = -16 + 16 + 7x + -7x

Combine like terms: -16 + 16 = 0
16 + -10x + x2 = 0 + 7x + -7x
16 + -10x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
16 + -10x + x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {2, 8}

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