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

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


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

Reorder the terms:
x(1 + 4x) = 3(x + 4)
(1 * x + 4x * x) = 3(x + 4)
(1x + 4x2) = 3(x + 4)

Reorder the terms:
1x + 4x2 = 3(4 + x)
1x + 4x2 = (4 * 3 + x * 3)
1x + 4x2 = (12 + 3x)

Solving
1x + 4x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 1x + -3x + 4x2 = 12 + 3x + -12 + -3x

Combine like terms: 1x + -3x = -2x
-12 + -2x + 4x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + -2x + 4x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + -2x + 4x2 = 0 + 3x + -3x
-12 + -2x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -1x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 2}

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