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

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


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

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

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

Multiply (-7 + x) * (-10 + x)
(-7(-10 + x) + x(-10 + x)) = 0
((-10 * -7 + x * -7) + x(-10 + x)) = 0
((70 + -7x) + x(-10 + x)) = 0
(70 + -7x + (-10 * x + x * x)) = 0
(70 + -7x + (-10x + x2)) = 0

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

Solving
70 + -17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

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

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