(x+7)(4x)=(x+7)(24)

Solution for (x+7)(4x)=(x+7)(24) equation:

Simplifying
(x + 7)(4x) = (x + 7)(24)

Reorder the terms:
(7 + x)(4x) = (x + 7)(24)

Remove parenthesis around (4x)
(7 + x) * 4x = (x + 7)(24)

Reorder the terms for easier multiplication:
4x(7 + x) = (x + 7)(24)
(7 * 4x + x * 4x) = (x + 7)(24)
(28x + 4x2) = (x + 7)(24)

Reorder the terms:
28x + 4x2 = (7 + x)(24)

Reorder the terms for easier multiplication:
28x + 4x2 = 24(7 + x)
28x + 4x2 = (7 * 24 + x * 24)
28x + 4x2 = (168 + 24x)

Solving
28x + 4x2 = 168 + 24x

Solving for variable 'x'.

Reorder the terms:
-168 + 28x + -24x + 4x2 = 168 + 24x + -168 + -24x

Combine like terms: 28x + -24x = 4x
-168 + 4x + 4x2 = 168 + 24x + -168 + -24x

Reorder the terms:
-168 + 4x + 4x2 = 168 + -168 + 24x + -24x

Combine like terms: 168 + -168 = 0
-168 + 4x + 4x2 = 0 + 24x + -24x
-168 + 4x + 4x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-168 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
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
Solution
x = {-7, 6}