(x-15)(x+5)=5229

Solution for (x-15)(x+5)=5229 equation:

Simplifying
(x + -15)(x + 5) = 5229

Reorder the terms:
(-15 + x)(x + 5) = 5229

Reorder the terms:
(-15 + x)(5 + x) = 5229

Multiply (-15 + x) * (5 + x)
(-15(5 + x) + x(5 + x)) = 5229
((5 * -15 + x * -15) + x(5 + x)) = 5229
((-75 + -15x) + x(5 + x)) = 5229
(-75 + -15x + (5 * x + x * x)) = 5229
(-75 + -15x + (5x + x2)) = 5229

Combine like terms: -15x + 5x = -10x
(-75 + -10x + x2) = 5229

Solving
-75 + -10x + x2 = 5229

Solving for variable 'x'.

Reorder the terms:
-75 + -5229 + -10x + x2 = 5229 + -5229

Combine like terms: -75 + -5229 = -5304
-5304 + -10x + x2 = 5229 + -5229

Combine like terms: 5229 + -5229 = 0
-5304 + -10x + x2 = 0

Factor a trinomial.
(-68 + -1x)(78 + -1x) = 0

Subproblem 1
Set the factor '(-68 + -1x)' equal to zero and attempt to solve:

Simplifying
-68 + -1x = 0

Solving
-68 + -1x = 0

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

Add '68' to each side of the equation.
-68 + 68 + -1x = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -1x = 0 + 68
-1x = 0 + 68

Combine like terms: 0 + 68 = 68
-1x = 68

Divide each side by '-1'.
x = -68

Simplifying
x = -68
Subproblem 2
Set the factor '(78 + -1x)' equal to zero and attempt to solve:

Simplifying
78 + -1x = 0

Solving
78 + -1x = 0

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

Add '-78' to each side of the equation.
78 + -78 + -1x = 0 + -78

Combine like terms: 78 + -78 = 0
0 + -1x = 0 + -78
-1x = 0 + -78

Combine like terms: 0 + -78 = -78
-1x = -78

Divide each side by '-1'.
x = 78

Simplifying
x = 78
Solution
x = {-68, 78}