(x-10)(x-5)=176

Solution for (x-10)(x-5)=176 equation:

Simplifying
(x + -10)(x + -5) = 176

Reorder the terms:
(-10 + x)(x + -5) = 176

Reorder the terms:
(-10 + x)(-5 + x) = 176

Multiply (-10 + x) * (-5 + x)
(-10(-5 + x) + x(-5 + x)) = 176
((-5 * -10 + x * -10) + x(-5 + x)) = 176
((50 + -10x) + x(-5 + x)) = 176
(50 + -10x + (-5 * x + x * x)) = 176
(50 + -10x + (-5x + x2)) = 176

Combine like terms: -10x + -5x = -15x
(50 + -15x + x2) = 176

Solving
50 + -15x + x2 = 176

Solving for variable 'x'.

Reorder the terms:
50 + -176 + -15x + x2 = 176 + -176

Combine like terms: 50 + -176 = -126
-126 + -15x + x2 = 176 + -176

Combine like terms: 176 + -176 = 0
-126 + -15x + x2 = 0

Factor a trinomial.
(-6 + -1x)(21 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-6, 21}