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

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

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

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

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

Multiply (-3 + x) * (6 + x)
(-3(6 + x) + x(6 + x)) = 10
((6 * -3 + x * -3) + x(6 + x)) = 10
((-18 + -3x) + x(6 + x)) = 10
(-18 + -3x + (6 * x + x * x)) = 10
(-18 + -3x + (6x + x2)) = 10

Combine like terms: -3x + 6x = 3x
(-18 + 3x + x2) = 10

Solving
-18 + 3x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-18 + -10 + 3x + x2 = 10 + -10

Combine like terms: -18 + -10 = -28
-28 + 3x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}