x(x-7)=2x-8

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Solution for x(x-7)=2x-8 equation: 


Simplifying
x(x + -7) = 2x + -8

Reorder the terms:
x(-7 + x) = 2x + -8
(-7 * x + x * x) = 2x + -8
(-7x + x2) = 2x + -8

Reorder the terms:
-7x + x2 = -8 + 2x

Solving
-7x + x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
8 + -7x + -2x + x2 = -8 + 2x + 8 + -2x

Combine like terms: -7x + -2x = -9x
8 + -9x + x2 = -8 + 2x + 8 + -2x

Reorder the terms:
8 + -9x + x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
8 + -9x + x2 = 0 + 2x + -2x
8 + -9x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
8 + -9x + x2 = 0

Factor a trinomial.
(1 + -1x)(8 + -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 '(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 = {1, 8}

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