510x+510(x+25)=17x(x+25)

Solution for 510x+510(x+25)=17x(x+25) equation:

Simplifying
510x + 510(x + 25) = 17x(x + 25)

Reorder the terms:
510x + 510(25 + x) = 17x(x + 25)
510x + (25 * 510 + x * 510) = 17x(x + 25)
510x + (12750 + 510x) = 17x(x + 25)

Reorder the terms:
12750 + 510x + 510x = 17x(x + 25)

Combine like terms: 510x + 510x = 1020x
12750 + 1020x = 17x(x + 25)

Reorder the terms:
12750 + 1020x = 17x(25 + x)
12750 + 1020x = (25 * 17x + x * 17x)
12750 + 1020x = (425x + 17x2)

Solving
12750 + 1020x = 425x + 17x2

Solving for variable 'x'.

Combine like terms: 1020x + -425x = 595x
12750 + 595x + -17x2 = 425x + 17x2 + -425x + -17x2

Reorder the terms:
12750 + 595x + -17x2 = 425x + -425x + 17x2 + -17x2

Combine like terms: 425x + -425x = 0
12750 + 595x + -17x2 = 0 + 17x2 + -17x2
12750 + 595x + -17x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
12750 + 595x + -17x2 = 0

Factor out the Greatest Common Factor (GCF), '17'.
17(750 + 35x + -1x2) = 0

Factor a trinomial.
17((50 + -1x)(15 + x)) = 0

Ignore the factor 17.
Subproblem 1
Set the factor '(50 + -1x)' equal to zero and attempt to solve:

Simplifying
50 + -1x = 0

Solving
50 + -1x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x = 0 + -50
-1x = 0 + -50

Combine like terms: 0 + -50 = -50
-1x = -50

Divide each side by '-1'.
x = 50

Simplifying
x = 50
Subproblem 2
Set the factor '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {50, -15}