(3x-5)(3x-5)=x+25

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Solution for (3x-5)(3x-5)=x+25 equation: 


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

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

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

Multiply (-5 + 3x) * (-5 + 3x)
(-5(-5 + 3x) + 3x * (-5 + 3x)) = x + 25
((-5 * -5 + 3x * -5) + 3x * (-5 + 3x)) = x + 25
((25 + -15x) + 3x * (-5 + 3x)) = x + 25
(25 + -15x + (-5 * 3x + 3x * 3x)) = x + 25
(25 + -15x + (-15x + 9x2)) = x + 25

Combine like terms: -15x + -15x = -30x
(25 + -30x + 9x2) = x + 25

Reorder the terms:
25 + -30x + 9x2 = 25 + x

Add '-25' to each side of the equation.
25 + -30x + -25 + 9x2 = 25 + -25 + x

Reorder the terms:
25 + -25 + -30x + 9x2 = 25 + -25 + x

Combine like terms: 25 + -25 = 0
0 + -30x + 9x2 = 25 + -25 + x
-30x + 9x2 = 25 + -25 + x

Combine like terms: 25 + -25 = 0
-30x + 9x2 = 0 + x
-30x + 9x2 = x

Solving
-30x + 9x2 = x

Solving for variable 'x'.

Reorder the terms:
-30x + -1x + 9x2 = x + -1x

Combine like terms: -30x + -1x = -31x
-31x + 9x2 = x + -1x

Combine like terms: x + -1x = 0
-31x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-31 + 9x) = 0


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

Subproblem 2
Set the factor '(-31 + 9x)' equal to zero and attempt to solve:

Simplifying
-31 + 9x = 0

Solving
-31 + 9x = 0

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

Add '31' to each side of the equation.
-31 + 31 + 9x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 9x = 0 + 31
9x = 0 + 31

Combine like terms: 0 + 31 = 31
9x = 31

Divide each side by '9'.
x = 3.444444444

Simplifying
x = 3.444444444
Solution
x = {0, 3.444444444}

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