(x+3)(x-7)=75

Solution for (x+3)(x-7)=75 equation:

Simplifying
(x + 3)(x + -7) = 75

Reorder the terms:
(3 + x)(x + -7) = 75

Reorder the terms:
(3 + x)(-7 + x) = 75

Multiply (3 + x) * (-7 + x)
(3(-7 + x) + x(-7 + x)) = 75
((-7 * 3 + x * 3) + x(-7 + x)) = 75
((-21 + 3x) + x(-7 + x)) = 75
(-21 + 3x + (-7 * x + x * x)) = 75
(-21 + 3x + (-7x + x2)) = 75

Combine like terms: 3x + -7x = -4x
(-21 + -4x + x2) = 75

Solving
-21 + -4x + x2 = 75

Solving for variable 'x'.

Reorder the terms:
-21 + -75 + -4x + x2 = 75 + -75

Combine like terms: -21 + -75 = -96
-96 + -4x + x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-96 + -4x + x2 = 0

Factor a trinomial.
(-8 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-8, 12}