(x+5)(x+3)(8)=(5)(3)(8)+34

Solution for (x+5)(x+3)(8)=(5)(3)(8)+34 equation:

Simplifying
(x + 5)(x + 3)(8) = (5)(3)(8) + 34

Reorder the terms:
(5 + x)(x + 3)(8) = (5)(3)(8) + 34

Reorder the terms:
(5 + x)(3 + x)(8) = (5)(3)(8) + 34

Reorder the terms for easier multiplication:
8(5 + x)(3 + x) = (5)(3)(8) + 34

Multiply (5 + x) * (3 + x)
8(5(3 + x) + x(3 + x)) = (5)(3)(8) + 34
8((3 * 5 + x * 5) + x(3 + x)) = (5)(3)(8) + 34
8((15 + 5x) + x(3 + x)) = (5)(3)(8) + 34
8(15 + 5x + (3 * x + x * x)) = (5)(3)(8) + 34
8(15 + 5x + (3x + x2)) = (5)(3)(8) + 34

Combine like terms: 5x + 3x = 8x
8(15 + 8x + x2) = (5)(3)(8) + 34
(15 * 8 + 8x * 8 + x2 * 8) = (5)(3)(8) + 34
(120 + 64x + 8x2) = (5)(3)(8) + 34

Multiply 5 * 3
120 + 64x + 8x2 = 15 * 8 + 34

Multiply 15 * 8
120 + 64x + 8x2 = 120 + 34

Combine like terms: 120 + 34 = 154
120 + 64x + 8x2 = 154

Solving
120 + 64x + 8x2 = 154

Solving for variable 'x'.

Reorder the terms:
120 + -154 + 64x + 8x2 = 154 + -154

Combine like terms: 120 + -154 = -34
-34 + 64x + 8x2 = 154 + -154

Combine like terms: 154 + -154 = 0
-34 + 64x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 32x + 4x2) = 0

Factor a trinomial.
2((-17 + -2x)(1 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve:

Simplifying
-17 + -2x = 0

Solving
-17 + -2x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -2x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2x = 0 + 17
-2x = 0 + 17

Combine like terms: 0 + 17 = 17
-2x = 17

Divide each side by '-2'.
x = -8.5

Simplifying
x = -8.5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-8.5, 0.5}