(x-10)(x-6)=-3

Solution for (x-10)(x-6)=-3 equation:

Simplifying
(x + -10)(x + -6) = -3

Reorder the terms:
(-10 + x)(x + -6) = -3

Reorder the terms:
(-10 + x)(-6 + x) = -3

Multiply (-10 + x) * (-6 + x)
(-10(-6 + x) + x(-6 + x)) = -3
((-6 * -10 + x * -10) + x(-6 + x)) = -3
((60 + -10x) + x(-6 + x)) = -3
(60 + -10x + (-6 * x + x * x)) = -3
(60 + -10x + (-6x + x2)) = -3

Combine like terms: -10x + -6x = -16x
(60 + -16x + x2) = -3

Solving
60 + -16x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
60 + 3 + -16x + x2 = -3 + 3

Combine like terms: 60 + 3 = 63
63 + -16x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
63 + -16x + x2 = 0

Factor a trinomial.
(7 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {7, 9}