5(x+1)3(x-2)=17

Solution for 5(x+1)3(x-2)=17 equation:

Simplifying
5(x + 1) * 3(x + -2) = 17

Reorder the terms:
5(1 + x) * 3(x + -2) = 17

Reorder the terms:
5(1 + x) * 3(-2 + x) = 17

Reorder the terms for easier multiplication:
5 * 3(1 + x)(-2 + x) = 17

Multiply 5 * 3
15(1 + x)(-2 + x) = 17

Multiply (1 + x) * (-2 + x)
15(1(-2 + x) + x(-2 + x)) = 17
15((-2 * 1 + x * 1) + x(-2 + x)) = 17
15((-2 + 1x) + x(-2 + x)) = 17
15(-2 + 1x + (-2 * x + x * x)) = 17
15(-2 + 1x + (-2x + x2)) = 17

Combine like terms: 1x + -2x = -1x
15(-2 + -1x + x2) = 17
(-2 * 15 + -1x * 15 + x2 * 15) = 17
(-30 + -15x + 15x2) = 17

Solving
-30 + -15x + 15x2 = 17

Solving for variable 'x'.

Reorder the terms:
-30 + -17 + -15x + 15x2 = 17 + -17

Combine like terms: -30 + -17 = -47
-47 + -15x + 15x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-47 + -15x + 15x2 = 0

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-3.133333333 + -1x + x2 = 0

Move the constant term to the right:

Add '3.133333333' to each side of the equation.
-3.133333333 + -1x + 3.133333333 + x2 = 0 + 3.133333333

Reorder the terms:
-3.133333333 + 3.133333333 + -1x + x2 = 0 + 3.133333333

Combine like terms: -3.133333333 + 3.133333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 3.133333333
-1x + x2 = 0 + 3.133333333

Combine like terms: 0 + 3.133333333 = 3.133333333
-1x + x2 = 3.133333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.133333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.133333333 + 0.25

Combine like terms: 3.133333333 + 0.25 = 3.383333333
0.25 + -1x + x2 = 3.383333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.383333333

Calculate the square root of the right side: 1.839383955

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.839383955 and -1.839383955.

Subproblem 1
x + -0.5 = 1.839383955

Simplifying
x + -0.5 = 1.839383955

Reorder the terms:
-0.5 + x = 1.839383955

Solving
-0.5 + x = 1.839383955

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.839383955 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.839383955 + 0.5
x = 1.839383955 + 0.5

Combine like terms: 1.839383955 + 0.5 = 2.339383955
x = 2.339383955

Simplifying
x = 2.339383955

Subproblem 2
x + -0.5 = -1.839383955

Simplifying
x + -0.5 = -1.839383955

Reorder the terms:
-0.5 + x = -1.839383955

Solving
-0.5 + x = -1.839383955

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.839383955 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.839383955 + 0.5
x = -1.839383955 + 0.5

Combine like terms: -1.839383955 + 0.5 = -1.339383955
x = -1.339383955

Simplifying
x = -1.339383955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.339383955, -1.339383955}