3(x+5)(x-10)=7

Solution for 3(x+5)(x-10)=7 equation:

Simplifying
3(x + 5)(x + -10) = 7

Reorder the terms:
3(5 + x)(x + -10) = 7

Reorder the terms:
3(5 + x)(-10 + x) = 7

Multiply (5 + x) * (-10 + x)
3(5(-10 + x) + x(-10 + x)) = 7
3((-10 * 5 + x * 5) + x(-10 + x)) = 7
3((-50 + 5x) + x(-10 + x)) = 7
3(-50 + 5x + (-10 * x + x * x)) = 7
3(-50 + 5x + (-10x + x2)) = 7

Combine like terms: 5x + -10x = -5x
3(-50 + -5x + x2) = 7
(-50 * 3 + -5x * 3 + x2 * 3) = 7
(-150 + -15x + 3x2) = 7

Solving
-150 + -15x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
-150 + -7 + -15x + 3x2 = 7 + -7

Combine like terms: -150 + -7 = -157
-157 + -15x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-157 + -15x + 3x2 = 0

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

Divide each side by '3'.
-52.33333333 + -5x + x2 = 0

Move the constant term to the right:

Add '52.33333333' to each side of the equation.
-52.33333333 + -5x + 52.33333333 + x2 = 0 + 52.33333333

Reorder the terms:
-52.33333333 + 52.33333333 + -5x + x2 = 0 + 52.33333333

Combine like terms: -52.33333333 + 52.33333333 = 0.00000000
0.00000000 + -5x + x2 = 0 + 52.33333333
-5x + x2 = 0 + 52.33333333

Combine like terms: 0 + 52.33333333 = 52.33333333
-5x + x2 = 52.33333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 52.33333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 52.33333333 + 6.25

Combine like terms: 52.33333333 + 6.25 = 58.58333333
6.25 + -5x + x2 = 58.58333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 58.58333333

Calculate the square root of the right side: 7.653975002

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.653975002 and -7.653975002.

Subproblem 1
x + -2.5 = 7.653975002

Simplifying
x + -2.5 = 7.653975002

Reorder the terms:
-2.5 + x = 7.653975002

Solving
-2.5 + x = 7.653975002

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.653975002 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.653975002 + 2.5
x = 7.653975002 + 2.5

Combine like terms: 7.653975002 + 2.5 = 10.153975002
x = 10.153975002

Simplifying
x = 10.153975002

Subproblem 2
x + -2.5 = -7.653975002

Simplifying
x + -2.5 = -7.653975002

Reorder the terms:
-2.5 + x = -7.653975002

Solving
-2.5 + x = -7.653975002

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.653975002 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.653975002 + 2.5
x = -7.653975002 + 2.5

Combine like terms: -7.653975002 + 2.5 = -5.153975002
x = -5.153975002

Simplifying
x = -5.153975002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.153975002, -5.153975002}