2x(4x+7)=30

Solution for 2x(4x+7)=30 equation:

Simplifying
2x(4x + 7) = 30

Reorder the terms:
2x(7 + 4x) = 30
(7 * 2x + 4x * 2x) = 30
(14x + 8x2) = 30

Solving
14x + 8x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 14x + 8x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 14x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 7x + 4x2) = 0

Factor a trinomial.
2((-3 + -1x)(5 + -4x)) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

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

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

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-3, 1.25}