(x+8)(x-5)=30

Solution for (x+8)(x-5)=30 equation:

Simplifying
(x + 8)(x + -5) = 30

Reorder the terms:
(8 + x)(x + -5) = 30

Reorder the terms:
(8 + x)(-5 + x) = 30

Multiply (8 + x) * (-5 + x)
(8(-5 + x) + x(-5 + x)) = 30
((-5 * 8 + x * 8) + x(-5 + x)) = 30
((-40 + 8x) + x(-5 + x)) = 30
(-40 + 8x + (-5 * x + x * x)) = 30
(-40 + 8x + (-5x + x2)) = 30

Combine like terms: 8x + -5x = 3x
(-40 + 3x + x2) = 30

Solving
-40 + 3x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
-40 + -30 + 3x + x2 = 30 + -30

Combine like terms: -40 + -30 = -70
-70 + 3x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-70 + 3x + x2 = 0

Factor a trinomial.
(-10 + -1x)(7 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-10, 7}