(x-3)(x-5)=35

Solution for (x-3)(x-5)=35 equation:

Simplifying
(x + -3)(x + -5) = 35

Reorder the terms:
(-3 + x)(x + -5) = 35

Reorder the terms:
(-3 + x)(-5 + x) = 35

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) = 35
((-5 * -3 + x * -3) + x(-5 + x)) = 35
((15 + -3x) + x(-5 + x)) = 35
(15 + -3x + (-5 * x + x * x)) = 35
(15 + -3x + (-5x + x2)) = 35

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) = 35

Solving
15 + -8x + x2 = 35

Solving for variable 'x'.

Reorder the terms:
15 + -35 + -8x + x2 = 35 + -35

Combine like terms: 15 + -35 = -20
-20 + -8x + x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-20 + -8x + x2 = 0

Factor a trinomial.
(-2 + -1x)(10 + -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 '(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 = {-2, 10}