15210=(78+x)(65+x)

Solution for 15210=(78+x)(65+x) equation:

Simplifying
15210 = (78 + x)(65 + x)

Multiply (78 + x) * (65 + x)
15210 = (78(65 + x) + x(65 + x))
15210 = ((65 * 78 + x * 78) + x(65 + x))
15210 = ((5070 + 78x) + x(65 + x))
15210 = (5070 + 78x + (65 * x + x * x))
15210 = (5070 + 78x + (65x + x2))

Combine like terms: 78x + 65x = 143x
15210 = (5070 + 143x + x2)

Solving
15210 = 5070 + 143x + x2

Solving for variable 'x'.

Combine like terms: 15210 + -5070 = 10140
10140 + -143x + -1x2 = 5070 + 143x + x2 + -5070 + -143x + -1x2

Reorder the terms:
10140 + -143x + -1x2 = 5070 + -5070 + 143x + -143x + x2 + -1x2

Combine like terms: 5070 + -5070 = 0
10140 + -143x + -1x2 = 0 + 143x + -143x + x2 + -1x2
10140 + -143x + -1x2 = 143x + -143x + x2 + -1x2

Combine like terms: 143x + -143x = 0
10140 + -143x + -1x2 = 0 + x2 + -1x2
10140 + -143x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10140 + -143x + -1x2 = 0

Factor a trinomial.
(52 + -1x)(195 + x) = 0

Subproblem 1
Set the factor '(52 + -1x)' equal to zero and attempt to solve:

Simplifying
52 + -1x = 0

Solving
52 + -1x = 0

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

Add '-52' to each side of the equation.
52 + -52 + -1x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -1x = 0 + -52
-1x = 0 + -52

Combine like terms: 0 + -52 = -52
-1x = -52

Divide each side by '-1'.
x = 52

Simplifying
x = 52
Subproblem 2
Set the factor '(195 + x)' equal to zero and attempt to solve:

Simplifying
195 + x = 0

Solving
195 + x = 0

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

Add '-195' to each side of the equation.
195 + -195 + x = 0 + -195

Combine like terms: 195 + -195 = 0
0 + x = 0 + -195
x = 0 + -195

Combine like terms: 0 + -195 = -195
x = -195

Simplifying
x = -195
Solution
x = {52, -195}