5x+48+7x=12x(x+4)

Solution for 5x+48+7x=12x(x+4) equation:

Simplifying
5x + 48 + 7x = 12x(x + 4)

Reorder the terms:
48 + 5x + 7x = 12x(x + 4)

Combine like terms: 5x + 7x = 12x
48 + 12x = 12x(x + 4)

Reorder the terms:
48 + 12x = 12x(4 + x)
48 + 12x = (4 * 12x + x * 12x)
48 + 12x = (48x + 12x2)

Solving
48 + 12x = 48x + 12x2

Solving for variable 'x'.

Combine like terms: 12x + -48x = -36x
48 + -36x + -12x2 = 48x + 12x2 + -48x + -12x2

Reorder the terms:
48 + -36x + -12x2 = 48x + -48x + 12x2 + -12x2

Combine like terms: 48x + -48x = 0
48 + -36x + -12x2 = 0 + 12x2 + -12x2
48 + -36x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
48 + -36x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + -3x + -1x2) = 0

Factor a trinomial.
12((1 + -1x)(4 + x)) = 0

Ignore the factor 12.
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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {1, -4}