(10x+2x)(2x+1)-(2x+50)=

Solution for (10x+2x)(2x+1)-(2x+50)= equation:

Simplifying
(10x + 2x)(2x + 1) + -1(2x + 50) = 0

Combine like terms: 10x + 2x = 12x
(12x)(2x + 1) + -1(2x + 50) = 0

Remove parenthesis around (12x)
12x(2x + 1) + -1(2x + 50) = 0

Reorder the terms:
12x(1 + 2x) + -1(2x + 50) = 0
(1 * 12x + 2x * 12x) + -1(2x + 50) = 0
(12x + 24x2) + -1(2x + 50) = 0

Reorder the terms:
12x + 24x2 + -1(50 + 2x) = 0
12x + 24x2 + (50 * -1 + 2x * -1) = 0
12x + 24x2 + (-50 + -2x) = 0

Reorder the terms:
-50 + 12x + -2x + 24x2 = 0

Combine like terms: 12x + -2x = 10x
-50 + 10x + 24x2 = 0

Solving
-50 + 10x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 5x + 12x2) = 0

Factor a trinomial.
2((-5 + -3x)(5 + -4x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667
Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-1.666666667, 1.25}