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

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


Simplifying
3x(4x + 1) + 1(4x + 1) = 0

Reorder the terms:
3x(1 + 4x) + 1(4x + 1) = 0
(1 * 3x + 4x * 3x) + 1(4x + 1) = 0
(3x + 12x2) + 1(4x + 1) = 0

Reorder the terms:
3x + 12x2 + 1(1 + 4x) = 0
3x + 12x2 + (1 * 1 + 4x * 1) = 0
3x + 12x2 + (1 + 4x) = 0

Reorder the terms:
1 + 3x + 4x + 12x2 = 0

Combine like terms: 3x + 4x = 7x
1 + 7x + 12x2 = 0

Solving
1 + 7x + 12x2 = 0

Solving for variable 'x'.

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


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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-0.3333333333, -0.25}

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