(3x-5)(3x-3)=-1

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Solution for (3x-5)(3x-3)=-1 equation: 


Simplifying
(3x + -5)(3x + -3) = -1

Reorder the terms:
(-5 + 3x)(3x + -3) = -1

Reorder the terms:
(-5 + 3x)(-3 + 3x) = -1

Multiply (-5 + 3x) * (-3 + 3x)
(-5(-3 + 3x) + 3x * (-3 + 3x)) = -1
((-3 * -5 + 3x * -5) + 3x * (-3 + 3x)) = -1
((15 + -15x) + 3x * (-3 + 3x)) = -1
(15 + -15x + (-3 * 3x + 3x * 3x)) = -1
(15 + -15x + (-9x + 9x2)) = -1

Combine like terms: -15x + -9x = -24x
(15 + -24x + 9x2) = -1

Solving
15 + -24x + 9x2 = -1

Solving for variable 'x'.

Reorder the terms:
15 + 1 + -24x + 9x2 = -1 + 1

Combine like terms: 15 + 1 = 16
16 + -24x + 9x2 = -1 + 1

Combine like terms: -1 + 1 = 0
16 + -24x + 9x2 = 0

Factor a trinomial.
(4 + -3x)(4 + -3x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {1.333333333, 1.333333333}

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