(45+x)(15+x)=(45-x)(15-x)

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Solution for (45+x)(15+x)=(45-x)(15-x) equation: 


Simplifying
(45 + x)(15 + x) = (45 + -1x)(15 + -1x)

Multiply (45 + x) * (15 + x)
(45(15 + x) + x(15 + x)) = (45 + -1x)(15 + -1x)
((15 * 45 + x * 45) + x(15 + x)) = (45 + -1x)(15 + -1x)
((675 + 45x) + x(15 + x)) = (45 + -1x)(15 + -1x)
(675 + 45x + (15 * x + x * x)) = (45 + -1x)(15 + -1x)
(675 + 45x + (15x + x2)) = (45 + -1x)(15 + -1x)

Combine like terms: 45x + 15x = 60x
(675 + 60x + x2) = (45 + -1x)(15 + -1x)

Multiply (45 + -1x) * (15 + -1x)
675 + 60x + x2 = (45(15 + -1x) + -1x * (15 + -1x))
675 + 60x + x2 = ((15 * 45 + -1x * 45) + -1x * (15 + -1x))
675 + 60x + x2 = ((675 + -45x) + -1x * (15 + -1x))
675 + 60x + x2 = (675 + -45x + (15 * -1x + -1x * -1x))
675 + 60x + x2 = (675 + -45x + (-15x + 1x2))

Combine like terms: -45x + -15x = -60x
675 + 60x + x2 = (675 + -60x + 1x2)

Add '-675' to each side of the equation.
675 + 60x + -675 + x2 = 675 + -60x + -675 + 1x2

Reorder the terms:
675 + -675 + 60x + x2 = 675 + -60x + -675 + 1x2

Combine like terms: 675 + -675 = 0
0 + 60x + x2 = 675 + -60x + -675 + 1x2
60x + x2 = 675 + -60x + -675 + 1x2

Reorder the terms:
60x + x2 = 675 + -675 + -60x + 1x2

Combine like terms: 675 + -675 = 0
60x + x2 = 0 + -60x + 1x2
60x + x2 = -60x + 1x2

Solving
60x + x2 = -60x + 1x2

Solving for variable 'x'.

Reorder the terms:
60x + 60x + x2 + -1x2 = -60x + 1x2 + 60x + -1x2

Combine like terms: 60x + 60x = 120x
120x + x2 + -1x2 = -60x + 1x2 + 60x + -1x2

Combine like terms: x2 + -1x2 = 0
120x + 0 = -60x + 1x2 + 60x + -1x2
120x = -60x + 1x2 + 60x + -1x2

Reorder the terms:
120x = -60x + 60x + 1x2 + -1x2

Combine like terms: -60x + 60x = 0
120x = 0 + 1x2 + -1x2
120x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
120x = 0

Ignore the factor 120.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Solution
x = {0}

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