x^2+3x=5x+48

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Solution for x^2+3x=5x+48 equation: 


Simplifying
x2 + 3x = 5x + 48

Reorder the terms:
3x + x2 = 5x + 48

Reorder the terms:
3x + x2 = 48 + 5x

Solving
3x + x2 = 48 + 5x

Solving for variable 'x'.

Reorder the terms:
-48 + 3x + -5x + x2 = 48 + 5x + -48 + -5x

Combine like terms: 3x + -5x = -2x
-48 + -2x + x2 = 48 + 5x + -48 + -5x

Reorder the terms:
-48 + -2x + x2 = 48 + -48 + 5x + -5x

Combine like terms: 48 + -48 = 0
-48 + -2x + x2 = 0 + 5x + -5x
-48 + -2x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-48 + -2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(8 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-6, 8}

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