5x+16=(3x-6)(3x-6)

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Solution for 5x+16=(3x-6)(3x-6) equation: 


Simplifying
5x + 16 = (3x + -6)(3x + -6)

Reorder the terms:
16 + 5x = (3x + -6)(3x + -6)

Reorder the terms:
16 + 5x = (-6 + 3x)(3x + -6)

Reorder the terms:
16 + 5x = (-6 + 3x)(-6 + 3x)

Multiply (-6 + 3x) * (-6 + 3x)
16 + 5x = (-6(-6 + 3x) + 3x * (-6 + 3x))
16 + 5x = ((-6 * -6 + 3x * -6) + 3x * (-6 + 3x))
16 + 5x = ((36 + -18x) + 3x * (-6 + 3x))
16 + 5x = (36 + -18x + (-6 * 3x + 3x * 3x))
16 + 5x = (36 + -18x + (-18x + 9x2))

Combine like terms: -18x + -18x = -36x
16 + 5x = (36 + -36x + 9x2)

Solving
16 + 5x = 36 + -36x + 9x2

Solving for variable 'x'.

Reorder the terms:
16 + -36 + 5x + 36x + -9x2 = 36 + -36x + 9x2 + -36 + 36x + -9x2

Combine like terms: 16 + -36 = -20
-20 + 5x + 36x + -9x2 = 36 + -36x + 9x2 + -36 + 36x + -9x2

Combine like terms: 5x + 36x = 41x
-20 + 41x + -9x2 = 36 + -36x + 9x2 + -36 + 36x + -9x2

Reorder the terms:
-20 + 41x + -9x2 = 36 + -36 + -36x + 36x + 9x2 + -9x2

Combine like terms: 36 + -36 = 0
-20 + 41x + -9x2 = 0 + -36x + 36x + 9x2 + -9x2
-20 + 41x + -9x2 = -36x + 36x + 9x2 + -9x2

Combine like terms: -36x + 36x = 0
-20 + 41x + -9x2 = 0 + 9x2 + -9x2
-20 + 41x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-20 + 41x + -9x2 = 0

Factor a trinomial.
(-4 + x)(5 + -9x) = 0


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

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + -9x)' equal to zero and attempt to solve:

Simplifying
5 + -9x = 0

Solving
5 + -9x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x = 0 + -5
-9x = 0 + -5

Combine like terms: 0 + -5 = -5
-9x = -5

Divide each side by '-9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {4, 0.5555555556}

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