4x(3x+1)=5

Solution for 4x(3x+1)=5 equation:

Simplifying
4x(3x + 1) = 5

Reorder the terms:
4x(1 + 3x) = 5
(1 * 4x + 3x * 4x) = 5
(4x + 12x2) = 5

Solving
4x + 12x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 4x + 12x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 4x + 12x2 = 0

Factor a trinomial.
(-5 + -6x)(1 + -2x) = 0

Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-0.8333333333, 0.5}