(3x-4)(3x-4)=16

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Solution for (3x-4)(3x-4)=16 equation: 


Simplifying
(3x + -4)(3x + -4) = 16

Reorder the terms:
(-4 + 3x)(3x + -4) = 16

Reorder the terms:
(-4 + 3x)(-4 + 3x) = 16

Multiply (-4 + 3x) * (-4 + 3x)
(-4(-4 + 3x) + 3x * (-4 + 3x)) = 16
((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) = 16
((16 + -12x) + 3x * (-4 + 3x)) = 16
(16 + -12x + (-4 * 3x + 3x * 3x)) = 16
(16 + -12x + (-12x + 9x2)) = 16

Combine like terms: -12x + -12x = -24x
(16 + -24x + 9x2) = 16

Add '-16' to each side of the equation.
16 + -24x + -16 + 9x2 = 16 + -16

Reorder the terms:
16 + -16 + -24x + 9x2 = 16 + -16

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

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

Solving
-24x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-8 + 3x) = 0

Ignore the factor 3.

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 '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Divide each side by '3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {0, 2.666666667}

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