225a=(a+90)(a+30)

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Solution for 225a=(a+90)(a+30) equation:


Simplifying
225a = (a + 90)(a + 30)

Reorder the terms:
225a = (90 + a)(a + 30)

Reorder the terms:
225a = (90 + a)(30 + a)

Multiply (90 + a) * (30 + a)
225a = (90(30 + a) + a(30 + a))
225a = ((30 * 90 + a * 90) + a(30 + a))
225a = ((2700 + 90a) + a(30 + a))
225a = (2700 + 90a + (30 * a + a * a))
225a = (2700 + 90a + (30a + a2))

Combine like terms: 90a + 30a = 120a
225a = (2700 + 120a + a2)

Solving
225a = 2700 + 120a + a2

Solving for variable 'a'.

Reorder the terms:
-2700 + 225a + -120a + -1a2 = 2700 + 120a + a2 + -2700 + -120a + -1a2

Combine like terms: 225a + -120a = 105a
-2700 + 105a + -1a2 = 2700 + 120a + a2 + -2700 + -120a + -1a2

Reorder the terms:
-2700 + 105a + -1a2 = 2700 + -2700 + 120a + -120a + a2 + -1a2

Combine like terms: 2700 + -2700 = 0
-2700 + 105a + -1a2 = 0 + 120a + -120a + a2 + -1a2
-2700 + 105a + -1a2 = 120a + -120a + a2 + -1a2

Combine like terms: 120a + -120a = 0
-2700 + 105a + -1a2 = 0 + a2 + -1a2
-2700 + 105a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-2700 + 105a + -1a2 = 0

Factor a trinomial.
(-60 + a)(45 + -1a) = 0


Subproblem 1
Set the factor '(-60 + a)' equal to zero and attempt to solve:

Simplifying
-60 + a = 0

Solving
-60 + a = 0

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

Add '60' to each side of the equation.
-60 + 60 + a = 0 + 60

Combine like terms: -60 + 60 = 0
0 + a = 0 + 60
a = 0 + 60

Combine like terms: 0 + 60 = 60
a = 60

Simplifying
a = 60

Subproblem 2
Set the factor '(45 + -1a)' equal to zero and attempt to solve:

Simplifying
45 + -1a = 0

Solving
45 + -1a = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1a = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1a = 0 + -45
-1a = 0 + -45

Combine like terms: 0 + -45 = -45
-1a = -45

Divide each side by '-1'.
a = 45

Simplifying
a = 45
Solution
a = {60, 45}

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