(2x+10)(-6x+15)=5+1

Solution for (2x+10)(-6x+15)=5+1 equation:

Simplifying
(2x + 10)(-6x + 15) = 5 + 1

Reorder the terms:
(10 + 2x)(-6x + 15) = 5 + 1

Reorder the terms:
(10 + 2x)(15 + -6x) = 5 + 1

Multiply (10 + 2x) * (15 + -6x)
(10(15 + -6x) + 2x * (15 + -6x)) = 5 + 1
((15 * 10 + -6x * 10) + 2x * (15 + -6x)) = 5 + 1
((150 + -60x) + 2x * (15 + -6x)) = 5 + 1
(150 + -60x + (15 * 2x + -6x * 2x)) = 5 + 1
(150 + -60x + (30x + -12x2)) = 5 + 1

Combine like terms: -60x + 30x = -30x
(150 + -30x + -12x2) = 5 + 1

Combine like terms: 5 + 1 = 6
150 + -30x + -12x2 = 6

Solving
150 + -30x + -12x2 = 6

Solving for variable 'x'.

Reorder the terms:
150 + -6 + -30x + -12x2 = 6 + -6

Combine like terms: 150 + -6 = 144
144 + -30x + -12x2 = 6 + -6

Combine like terms: 6 + -6 = 0
144 + -30x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(24 + -5x + -2x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(24 + -5x + -2x2)' equal to zero and attempt to solve:

Simplifying
24 + -5x + -2x2 = 0

Solving
24 + -5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-12 + 2.5x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 2.5x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 2.5x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 2.5x + x2 = 0 + 12
2.5x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
2.5x + x2 = 12

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 12 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 12 + 1.5625

Combine like terms: 12 + 1.5625 = 13.5625
1.5625 + 2.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.682729966 and -3.682729966.

Subproblem 1
x + 1.25 = 3.682729966

Simplifying
x + 1.25 = 3.682729966

Reorder the terms:
1.25 + x = 3.682729966

Solving
1.25 + x = 3.682729966

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 3.682729966 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 3.682729966 + -1.25
x = 3.682729966 + -1.25

Combine like terms: 3.682729966 + -1.25 = 2.432729966
x = 2.432729966

Simplifying
x = 2.432729966

Subproblem 2
x + 1.25 = -3.682729966

Simplifying
x + 1.25 = -3.682729966

Reorder the terms:
1.25 + x = -3.682729966

Solving
1.25 + x = -3.682729966

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -3.682729966 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -3.682729966 + -1.25
x = -3.682729966 + -1.25

Combine like terms: -3.682729966 + -1.25 = -4.932729966
x = -4.932729966

Simplifying
x = -4.932729966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.432729966, -4.932729966}
Solution
x = {2.432729966, -4.932729966}