3x(4x+6)=30

Solution for 3x(4x+6)=30 equation:

Simplifying
3x(4x + 6) = 30

Reorder the terms:
3x(6 + 4x) = 30
(6 * 3x + 4x * 3x) = 30
(18x + 12x2) = 30

Solving
18x + 12x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 18x + 12x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 18x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 3x + 2x2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
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
Solution
x = {-2.5, 1}