6(x+4)=30x+6(x^2+7)

Solution for 6(x+4)=30x+6(x^2+7) equation:

Simplifying
6(x + 4) = 30x + 6(x2 + 7)

Reorder the terms:
6(4 + x) = 30x + 6(x2 + 7)
(4 * 6 + x * 6) = 30x + 6(x2 + 7)
(24 + 6x) = 30x + 6(x2 + 7)

Reorder the terms:
24 + 6x = 30x + 6(7 + x2)
24 + 6x = 30x + (7 * 6 + x2 * 6)
24 + 6x = 30x + (42 + 6x2)

Reorder the terms:
24 + 6x = 42 + 30x + 6x2

Solving
24 + 6x = 42 + 30x + 6x2

Solving for variable 'x'.

Reorder the terms:
24 + -42 + 6x + -30x + -6x2 = 42 + 30x + 6x2 + -42 + -30x + -6x2

Combine like terms: 24 + -42 = -18
-18 + 6x + -30x + -6x2 = 42 + 30x + 6x2 + -42 + -30x + -6x2

Combine like terms: 6x + -30x = -24x
-18 + -24x + -6x2 = 42 + 30x + 6x2 + -42 + -30x + -6x2

Reorder the terms:
-18 + -24x + -6x2 = 42 + -42 + 30x + -30x + 6x2 + -6x2

Combine like terms: 42 + -42 = 0
-18 + -24x + -6x2 = 0 + 30x + -30x + 6x2 + -6x2
-18 + -24x + -6x2 = 30x + -30x + 6x2 + -6x2

Combine like terms: 30x + -30x = 0
-18 + -24x + -6x2 = 0 + 6x2 + -6x2
-18 + -24x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-18 + -24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-6'.
-6(3 + 4x + x2) = 0

Factor a trinomial.
-6((3 + x)(1 + x)) = 0

Ignore the factor -6.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-3, -1}