81x^2-72x+16-(9x-4)(3x-5)=0

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Solution for 81x^2-72x+16-(9x-4)(3x-5)=0 equation: 


Simplifying
81x2 + -72x + 16 + -1(9x + -4)(3x + -5) = 0

Reorder the terms:
81x2 + -72x + 16 + -1(-4 + 9x)(3x + -5) = 0

Reorder the terms:
81x2 + -72x + 16 + -1(-4 + 9x)(-5 + 3x) = 0

Multiply (-4 + 9x) * (-5 + 3x)
81x2 + -72x + 16 + -1(-4(-5 + 3x) + 9x * (-5 + 3x)) = 0
81x2 + -72x + 16 + -1((-5 * -4 + 3x * -4) + 9x * (-5 + 3x)) = 0
81x2 + -72x + 16 + -1((20 + -12x) + 9x * (-5 + 3x)) = 0
81x2 + -72x + 16 + -1(20 + -12x + (-5 * 9x + 3x * 9x)) = 0
81x2 + -72x + 16 + -1(20 + -12x + (-45x + 27x2)) = 0

Combine like terms: -12x + -45x = -57x
81x2 + -72x + 16 + -1(20 + -57x + 27x2) = 0
81x2 + -72x + 16 + (20 * -1 + -57x * -1 + 27x2 * -1) = 0
81x2 + -72x + 16 + (-20 + 57x + -27x2) = 0

Reorder the terms:
16 + -20 + -72x + 57x + 81x2 + -27x2 = 0

Combine like terms: 16 + -20 = -4
-4 + -72x + 57x + 81x2 + -27x2 = 0

Combine like terms: -72x + 57x = -15x
-4 + -15x + 81x2 + -27x2 = 0

Combine like terms: 81x2 + -27x2 = 54x2
-4 + -15x + 54x2 = 0

Solving
-4 + -15x + 54x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -6x)(4 + -9x) = 0


Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

Subproblem 2
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 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 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444
Solution
x = {-0.1666666667, 0.4444444444}

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