7x(x+3)=8x+24

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Solution for 7x(x+3)=8x+24 equation: 


Simplifying
7x(x + 3) = 8x + 24

Reorder the terms:
7x(3 + x) = 8x + 24
(3 * 7x + x * 7x) = 8x + 24
(21x + 7x2) = 8x + 24

Reorder the terms:
21x + 7x2 = 24 + 8x

Solving
21x + 7x2 = 24 + 8x

Solving for variable 'x'.

Reorder the terms:
-24 + 21x + -8x + 7x2 = 24 + 8x + -24 + -8x

Combine like terms: 21x + -8x = 13x
-24 + 13x + 7x2 = 24 + 8x + -24 + -8x

Reorder the terms:
-24 + 13x + 7x2 = 24 + -24 + 8x + -8x

Combine like terms: 24 + -24 = 0
-24 + 13x + 7x2 = 0 + 8x + -8x
-24 + 13x + 7x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-24 + 13x + 7x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -7x) = 0


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 '(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 = {-3, 1.142857143}

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