124-(15x-10)*(2x+13)=170-(110x+121)*(5x-60)

Solution for 124-(15x-10)*(2x+13)=170-(110x+121)*(5x-60) equation:

Simplifying
124 + -1(15x + -10)(2x + 13) = 170 + -1(110x + 121)(5x + -60)

Reorder the terms:
124 + -1(-10 + 15x)(2x + 13) = 170 + -1(110x + 121)(5x + -60)

Reorder the terms:
124 + -1(-10 + 15x)(13 + 2x) = 170 + -1(110x + 121)(5x + -60)

Multiply (-10 + 15x) * (13 + 2x)
124 + -1(-10(13 + 2x) + 15x * (13 + 2x)) = 170 + -1(110x + 121)(5x + -60)
124 + -1((13 * -10 + 2x * -10) + 15x * (13 + 2x)) = 170 + -1(110x + 121)(5x + -60)
124 + -1((-130 + -20x) + 15x * (13 + 2x)) = 170 + -1(110x + 121)(5x + -60)
124 + -1(-130 + -20x + (13 * 15x + 2x * 15x)) = 170 + -1(110x + 121)(5x + -60)
124 + -1(-130 + -20x + (195x + 30x2)) = 170 + -1(110x + 121)(5x + -60)

Combine like terms: -20x + 195x = 175x
124 + -1(-130 + 175x + 30x2) = 170 + -1(110x + 121)(5x + -60)
124 + (-130 * -1 + 175x * -1 + 30x2 * -1) = 170 + -1(110x + 121)(5x + -60)
124 + (130 + -175x + -30x2) = 170 + -1(110x + 121)(5x + -60)

Combine like terms: 124 + 130 = 254
254 + -175x + -30x2 = 170 + -1(110x + 121)(5x + -60)

Reorder the terms:
254 + -175x + -30x2 = 170 + -1(121 + 110x)(5x + -60)

Reorder the terms:
254 + -175x + -30x2 = 170 + -1(121 + 110x)(-60 + 5x)

Multiply (121 + 110x) * (-60 + 5x)
254 + -175x + -30x2 = 170 + -1(121(-60 + 5x) + 110x * (-60 + 5x))
254 + -175x + -30x2 = 170 + -1((-60 * 121 + 5x * 121) + 110x * (-60 + 5x))
254 + -175x + -30x2 = 170 + -1((-7260 + 605x) + 110x * (-60 + 5x))
254 + -175x + -30x2 = 170 + -1(-7260 + 605x + (-60 * 110x + 5x * 110x))
254 + -175x + -30x2 = 170 + -1(-7260 + 605x + (-6600x + 550x2))

Combine like terms: 605x + -6600x = -5995x
254 + -175x + -30x2 = 170 + -1(-7260 + -5995x + 550x2)
254 + -175x + -30x2 = 170 + (-7260 * -1 + -5995x * -1 + 550x2 * -1)
254 + -175x + -30x2 = 170 + (7260 + 5995x + -550x2)

Combine like terms: 170 + 7260 = 7430
254 + -175x + -30x2 = 7430 + 5995x + -550x2

Solving
254 + -175x + -30x2 = 7430 + 5995x + -550x2

Solving for variable 'x'.

Reorder the terms:
254 + -7430 + -175x + -5995x + -30x2 + 550x2 = 7430 + 5995x + -550x2 + -7430 + -5995x + 550x2

Combine like terms: 254 + -7430 = -7176
-7176 + -175x + -5995x + -30x2 + 550x2 = 7430 + 5995x + -550x2 + -7430 + -5995x + 550x2

Combine like terms: -175x + -5995x = -6170x
-7176 + -6170x + -30x2 + 550x2 = 7430 + 5995x + -550x2 + -7430 + -5995x + 550x2

Combine like terms: -30x2 + 550x2 = 520x2
-7176 + -6170x + 520x2 = 7430 + 5995x + -550x2 + -7430 + -5995x + 550x2

Reorder the terms:
-7176 + -6170x + 520x2 = 7430 + -7430 + 5995x + -5995x + -550x2 + 550x2

Combine like terms: 7430 + -7430 = 0
-7176 + -6170x + 520x2 = 0 + 5995x + -5995x + -550x2 + 550x2
-7176 + -6170x + 520x2 = 5995x + -5995x + -550x2 + 550x2

Combine like terms: 5995x + -5995x = 0
-7176 + -6170x + 520x2 = 0 + -550x2 + 550x2
-7176 + -6170x + 520x2 = -550x2 + 550x2

Combine like terms: -550x2 + 550x2 = 0
-7176 + -6170x + 520x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3588 + -3085x + 260x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3588 + -3085x + 260x2)' equal to zero and attempt to solve:

Simplifying
-3588 + -3085x + 260x2 = 0

Solving
-3588 + -3085x + 260x2 = 0

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

Divide each side by '260'.
-13.8 + -11.86538462x + x2 = 0.0

Move the constant term to the right:

Add '13.8' to each side of the equation.
-13.8 + -11.86538462x + 13.8 + x2 = 0.0 + 13.8

Reorder the terms:
-13.8 + 13.8 + -11.86538462x + x2 = 0.0 + 13.8

Combine like terms: -13.8 + 13.8 = 0.0
0.0 + -11.86538462x + x2 = 0.0 + 13.8
-11.86538462x + x2 = 0.0 + 13.8

Combine like terms: 0.0 + 13.8 = 13.8
-11.86538462x + x2 = 13.8

The x term is -11.86538462x.  Take half its coefficient (-5.93269231).
Square it (35.19683805) and add it to both sides.

Add '35.19683805' to each side of the equation.
-11.86538462x + 35.19683805 + x2 = 13.8 + 35.19683805

Reorder the terms:
35.19683805 + -11.86538462x + x2 = 13.8 + 35.19683805

Combine like terms: 13.8 + 35.19683805 = 48.99683805
35.19683805 + -11.86538462x + x2 = 48.99683805

Factor a perfect square on the left side:
(x + -5.93269231)(x + -5.93269231) = 48.99683805

Calculate the square root of the right side: 6.999774143

Break this problem into two subproblems by setting 
(x + -5.93269231) equal to 6.999774143 and -6.999774143.

Subproblem 1
x + -5.93269231 = 6.999774143

Simplifying
x + -5.93269231 = 6.999774143

Reorder the terms:
-5.93269231 + x = 6.999774143

Solving
-5.93269231 + x = 6.999774143

Solving for variable 'x'.

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

Add '5.93269231' to each side of the equation.
-5.93269231 + 5.93269231 + x = 6.999774143 + 5.93269231

Combine like terms: -5.93269231 + 5.93269231 = 0.00000000
0.00000000 + x = 6.999774143 + 5.93269231
x = 6.999774143 + 5.93269231

Combine like terms: 6.999774143 + 5.93269231 = 12.932466453
x = 12.932466453

Simplifying
x = 12.932466453

Subproblem 2
x + -5.93269231 = -6.999774143

Simplifying
x + -5.93269231 = -6.999774143

Reorder the terms:
-5.93269231 + x = -6.999774143

Solving
-5.93269231 + x = -6.999774143

Solving for variable 'x'.

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

Add '5.93269231' to each side of the equation.
-5.93269231 + 5.93269231 + x = -6.999774143 + 5.93269231

Combine like terms: -5.93269231 + 5.93269231 = 0.00000000
0.00000000 + x = -6.999774143 + 5.93269231
x = -6.999774143 + 5.93269231

Combine like terms: -6.999774143 + 5.93269231 = -1.067081833
x = -1.067081833

Simplifying
x = -1.067081833

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.932466453, -1.067081833}
Solution
x = {12.932466453, -1.067081833}