3(4x+1)(4x+1)=48

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Solution for 3(4x+1)(4x+1)=48 equation: 


Simplifying
3(4x + 1)(4x + 1) = 48

Reorder the terms:
3(1 + 4x)(4x + 1) = 48

Reorder the terms:
3(1 + 4x)(1 + 4x) = 48

Multiply (1 + 4x) * (1 + 4x)
3(1(1 + 4x) + 4x * (1 + 4x)) = 48
3((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = 48
3((1 + 4x) + 4x * (1 + 4x)) = 48
3(1 + 4x + (1 * 4x + 4x * 4x)) = 48
3(1 + 4x + (4x + 16x2)) = 48

Combine like terms: 4x + 4x = 8x
3(1 + 8x + 16x2) = 48
(1 * 3 + 8x * 3 + 16x2 * 3) = 48
(3 + 24x + 48x2) = 48

Solving
3 + 24x + 48x2 = 48

Solving for variable 'x'.

Reorder the terms:
3 + -48 + 24x + 48x2 = 48 + -48

Combine like terms: 3 + -48 = -45
-45 + 24x + 48x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-45 + 24x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 8x + 16x2) = 0

Factor a trinomial.
3((-5 + -4x)(3 + -4x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.25, 0.75}

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