(3x+4)(3x+4)-16=0

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Solution for (3x+4)(3x+4)-16=0 equation: 


Simplifying
(3x + 4)(3x + 4) + -16 = 0

Reorder the terms:
(4 + 3x)(3x + 4) + -16 = 0

Reorder the terms:
(4 + 3x)(4 + 3x) + -16 = 0

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) + -16 = 0
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) + -16 = 0
((16 + 12x) + 3x * (4 + 3x)) + -16 = 0
(16 + 12x + (4 * 3x + 3x * 3x)) + -16 = 0
(16 + 12x + (12x + 9x2)) + -16 = 0

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) + -16 = 0

Reorder the terms:
16 + -16 + 24x + 9x2 = 0

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