(3x+4)(3x+4)=64

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Solution for (3x+4)(3x+4)=64 equation: 


Simplifying
(3x + 4)(3x + 4) = 64

Reorder the terms:
(4 + 3x)(3x + 4) = 64

Reorder the terms:
(4 + 3x)(4 + 3x) = 64

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) = 64
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 64
((16 + 12x) + 3x * (4 + 3x)) = 64
(16 + 12x + (4 * 3x + 3x * 3x)) = 64
(16 + 12x + (12x + 9x2)) = 64

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) = 64

Solving
16 + 24x + 9x2 = 64

Solving for variable 'x'.

Reorder the terms:
16 + -64 + 24x + 9x2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + 24x + 9x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + 24x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 8x + 3x2) = 0

Factor a trinomial.
3((-4 + -1x)(4 + -3x)) = 0

Ignore the factor 3.

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 1.333333333}

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