3x^2-24x+48=10x-32

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Solution for 3x^2-24x+48=10x-32 equation: 


Simplifying
3x2 + -24x + 48 = 10x + -32

Reorder the terms:
48 + -24x + 3x2 = 10x + -32

Reorder the terms:
48 + -24x + 3x2 = -32 + 10x

Solving
48 + -24x + 3x2 = -32 + 10x

Solving for variable 'x'.

Reorder the terms:
48 + 32 + -24x + -10x + 3x2 = -32 + 10x + 32 + -10x

Combine like terms: 48 + 32 = 80
80 + -24x + -10x + 3x2 = -32 + 10x + 32 + -10x

Combine like terms: -24x + -10x = -34x
80 + -34x + 3x2 = -32 + 10x + 32 + -10x

Reorder the terms:
80 + -34x + 3x2 = -32 + 32 + 10x + -10x

Combine like terms: -32 + 32 = 0
80 + -34x + 3x2 = 0 + 10x + -10x
80 + -34x + 3x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
80 + -34x + 3x2 = 0

Factor a trinomial.
(10 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333

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 = {3.333333333, 8}

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