8(x+3)*23(x-7)=

Solution for 8(x+3)*23(x-7)= equation:

Simplifying
8(x + 3) * 23(x + -7) = 0

Reorder the terms:
8(3 + x) * 23(x + -7) = 0

Reorder the terms:
8(3 + x) * 23(-7 + x) = 0

Reorder the terms for easier multiplication:
8 * 23(3 + x)(-7 + x) = 0

Multiply 8 * 23
184(3 + x)(-7 + x) = 0

Multiply (3 + x) * (-7 + x)
184(3(-7 + x) + x(-7 + x)) = 0
184((-7 * 3 + x * 3) + x(-7 + x)) = 0
184((-21 + 3x) + x(-7 + x)) = 0
184(-21 + 3x + (-7 * x + x * x)) = 0
184(-21 + 3x + (-7x + x2)) = 0

Combine like terms: 3x + -7x = -4x
184(-21 + -4x + x2) = 0
(-21 * 184 + -4x * 184 + x2 * 184) = 0
(-3864 + -736x + 184x2) = 0

Solving
-3864 + -736x + 184x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '184'.
184(-21 + -4x + x2) = 0

Factor a trinomial.
184((-3 + -1x)(7 + -1x)) = 0

Ignore the factor 184.
Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 7}