5x(x+4)=3(6x+1)

Solution for 5x(x+4)=3(6x+1) equation:

Simplifying
5x(x + 4) = 3(6x + 1)

Reorder the terms:
5x(4 + x) = 3(6x + 1)
(4 * 5x + x * 5x) = 3(6x + 1)
(20x + 5x2) = 3(6x + 1)

Reorder the terms:
20x + 5x2 = 3(1 + 6x)
20x + 5x2 = (1 * 3 + 6x * 3)
20x + 5x2 = (3 + 18x)

Solving
20x + 5x2 = 3 + 18x

Solving for variable 'x'.

Reorder the terms:
-3 + 20x + -18x + 5x2 = 3 + 18x + -3 + -18x

Combine like terms: 20x + -18x = 2x
-3 + 2x + 5x2 = 3 + 18x + -3 + -18x

Reorder the terms:
-3 + 2x + 5x2 = 3 + -3 + 18x + -18x

Combine like terms: 3 + -3 = 0
-3 + 2x + 5x2 = 0 + 18x + -18x
-3 + 2x + 5x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-3 + 2x + 5x2 = 0

Factor a trinomial.
(-1 + -1x)(3 + -5x) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-1, 0.6}