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

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

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

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

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

Multiply (15 + 5x) * (-10 + 6x)
x = (15(-10 + 6x) + 5x * (-10 + 6x))
x = ((-10 * 15 + 6x * 15) + 5x * (-10 + 6x))
x = ((-150 + 90x) + 5x * (-10 + 6x))
x = (-150 + 90x + (-10 * 5x + 6x * 5x))
x = (-150 + 90x + (-50x + 30x2))

Combine like terms: 90x + -50x = 40x
x = (-150 + 40x + 30x2)

Solving
x = -150 + 40x + 30x2

Solving for variable 'x'.

Reorder the terms:
150 + x + -40x + -30x2 = -150 + 40x + 30x2 + 150 + -40x + -30x2

Combine like terms: x + -40x = -39x
150 + -39x + -30x2 = -150 + 40x + 30x2 + 150 + -40x + -30x2

Reorder the terms:
150 + -39x + -30x2 = -150 + 150 + 40x + -40x + 30x2 + -30x2

Combine like terms: -150 + 150 = 0
150 + -39x + -30x2 = 0 + 40x + -40x + 30x2 + -30x2
150 + -39x + -30x2 = 40x + -40x + 30x2 + -30x2

Combine like terms: 40x + -40x = 0
150 + -39x + -30x2 = 0 + 30x2 + -30x2
150 + -39x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
150 + -39x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(50 + -13x + -10x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(50 + -13x + -10x2)' equal to zero and attempt to solve:

Simplifying
50 + -13x + -10x2 = 0

Solving
50 + -13x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-5 + 1.3x + x2 = 0.0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 1.3x + 5 + x2 = 0.0 + 5

Reorder the terms:
-5 + 5 + 1.3x + x2 = 0.0 + 5

Combine like terms: -5 + 5 = 0
0 + 1.3x + x2 = 0.0 + 5
1.3x + x2 = 0.0 + 5

Combine like terms: 0.0 + 5 = 5
1.3x + x2 = 5

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 5 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 5 + 0.4225

Combine like terms: 5 + 0.4225 = 5.4225
0.4225 + 1.3x + x2 = 5.4225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 5.4225

Calculate the square root of the right side: 2.328626204

Break this problem into two subproblems by setting 
(x + 0.65) equal to 2.328626204 and -2.328626204.

Subproblem 1
x + 0.65 = 2.328626204

Simplifying
x + 0.65 = 2.328626204

Reorder the terms:
0.65 + x = 2.328626204

Solving
0.65 + x = 2.328626204

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 2.328626204 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 2.328626204 + -0.65
x = 2.328626204 + -0.65

Combine like terms: 2.328626204 + -0.65 = 1.678626204
x = 1.678626204

Simplifying
x = 1.678626204

Subproblem 2
x + 0.65 = -2.328626204

Simplifying
x + 0.65 = -2.328626204

Reorder the terms:
0.65 + x = -2.328626204

Solving
0.65 + x = -2.328626204

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -2.328626204 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -2.328626204 + -0.65
x = -2.328626204 + -0.65

Combine like terms: -2.328626204 + -0.65 = -2.978626204
x = -2.978626204

Simplifying
x = -2.978626204

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.678626204, -2.978626204}
Solution
x = {1.678626204, -2.978626204}