x(x-7)-8(x-7)=0

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Solution for x(x-7)-8(x-7)=0 equation: 


Simplifying
x(x + -7) + -8(x + -7) = 0

Reorder the terms:
x(-7 + x) + -8(x + -7) = 0
(-7 * x + x * x) + -8(x + -7) = 0
(-7x + x2) + -8(x + -7) = 0

Reorder the terms:
-7x + x2 + -8(-7 + x) = 0
-7x + x2 + (-7 * -8 + x * -8) = 0
-7x + x2 + (56 + -8x) = 0

Reorder the terms:
56 + -7x + -8x + x2 = 0

Combine like terms: -7x + -8x = -15x
56 + -15x + x2 = 0

Solving
56 + -15x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(8 + -1x) = 0


Subproblem 1
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

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 = {7, 8}

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