(3a-5)(3a-5)=25

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Solution for (3a-5)(3a-5)=25 equation:


Simplifying
(3a + -5)(3a + -5) = 25

Reorder the terms:
(-5 + 3a)(3a + -5) = 25

Reorder the terms:
(-5 + 3a)(-5 + 3a) = 25

Multiply (-5 + 3a) * (-5 + 3a)
(-5(-5 + 3a) + 3a * (-5 + 3a)) = 25
((-5 * -5 + 3a * -5) + 3a * (-5 + 3a)) = 25
((25 + -15a) + 3a * (-5 + 3a)) = 25
(25 + -15a + (-5 * 3a + 3a * 3a)) = 25
(25 + -15a + (-15a + 9a2)) = 25

Combine like terms: -15a + -15a = -30a
(25 + -30a + 9a2) = 25

Add '-25' to each side of the equation.
25 + -30a + -25 + 9a2 = 25 + -25

Reorder the terms:
25 + -25 + -30a + 9a2 = 25 + -25

Combine like terms: 25 + -25 = 0
0 + -30a + 9a2 = 25 + -25
-30a + 9a2 = 25 + -25

Combine like terms: 25 + -25 = 0
-30a + 9a2 = 0

Solving
-30a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-10 + 3a) = 0

Ignore the factor 3.

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(-10 + 3a)' equal to zero and attempt to solve:

Simplifying
-10 + 3a = 0

Solving
-10 + 3a = 0

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

Add '10' to each side of the equation.
-10 + 10 + 3a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3a = 0 + 10
3a = 0 + 10

Combine like terms: 0 + 10 = 10
3a = 10

Divide each side by '3'.
a = 3.333333333

Simplifying
a = 3.333333333
Solution
a = {0, 3.333333333}

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