10(x-7)-x(x-7)=0

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Solution for 10(x-7)-x(x-7)=0 equation: 


Simplifying
10(x + -7) + -1x(x + -7) = 0

Reorder the terms:
10(-7 + x) + -1x(x + -7) = 0
(-7 * 10 + x * 10) + -1x(x + -7) = 0
(-70 + 10x) + -1x(x + -7) = 0

Reorder the terms:
-70 + 10x + -1x(-7 + x) = 0
-70 + 10x + (-7 * -1x + x * -1x) = 0
-70 + 10x + (7x + -1x2) = 0

Combine like terms: 10x + 7x = 17x
-70 + 17x + -1x2 = 0

Solving
-70 + 17x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + x)(7 + -1x) = 0


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

Simplifying
-10 + x = 0

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

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

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

Simplifying
x = 10

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {10, 7}

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