(4x+1)(3x)=54

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Solution for (4x+1)(3x)=54 equation: 


Simplifying
(4x + 1)(3x) = 54

Reorder the terms:
(1 + 4x)(3x) = 54

Remove parenthesis around (3x)
(1 + 4x) * 3x = 54

Reorder the terms for easier multiplication:
3x(1 + 4x) = 54
(1 * 3x + 4x * 3x) = 54
(3x + 12x2) = 54

Solving
3x + 12x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 3x + 12x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 3x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + x + 4x2) = 0

Factor a trinomial.
3((-9 + -4x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.25, 2}

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