7x(x+6)=8x+48

Solution for 7x(x+6)=8x+48 equation:

Simplifying
7x(x + 6) = 8x + 48

Reorder the terms:
7x(6 + x) = 8x + 48
(6 * 7x + x * 7x) = 8x + 48
(42x + 7x2) = 8x + 48

Reorder the terms:
42x + 7x2 = 48 + 8x

Solving
42x + 7x2 = 48 + 8x

Solving for variable 'x'.

Reorder the terms:
-48 + 42x + -8x + 7x2 = 48 + 8x + -48 + -8x

Combine like terms: 42x + -8x = 34x
-48 + 34x + 7x2 = 48 + 8x + -48 + -8x

Reorder the terms:
-48 + 34x + 7x2 = 48 + -48 + 8x + -8x

Combine like terms: 48 + -48 = 0
-48 + 34x + 7x2 = 0 + 8x + -8x
-48 + 34x + 7x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-48 + 34x + 7x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -7x) = 0

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(8 + -7x)' equal to zero and attempt to solve:

Simplifying
8 + -7x = 0

Solving
8 + -7x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x = 0 + -8
-7x = 0 + -8

Combine like terms: 0 + -8 = -8
-7x = -8

Divide each side by '-7'.
x = 1.142857143

Simplifying
x = 1.142857143
Solution
x = {-6, 1.142857143}