10=5x^2-3x+2

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Solution for 10=5x^2-3x+2 equation: 


Simplifying
10 = 5x2 + -3x + 2

Reorder the terms:
10 = 2 + -3x + 5x2

Solving
10 = 2 + -3x + 5x2

Solving for variable 'x'.

Combine like terms: 10 + -2 = 8
8 + 3x + -5x2 = 2 + -3x + 5x2 + -2 + 3x + -5x2

Reorder the terms:
8 + 3x + -5x2 = 2 + -2 + -3x + 3x + 5x2 + -5x2

Combine like terms: 2 + -2 = 0
8 + 3x + -5x2 = 0 + -3x + 3x + 5x2 + -5x2
8 + 3x + -5x2 = -3x + 3x + 5x2 + -5x2

Combine like terms: -3x + 3x = 0
8 + 3x + -5x2 = 0 + 5x2 + -5x2
8 + 3x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
8 + 3x + -5x2 = 0

Factor a trinomial.
(8 + -5x)(1 + x) = 0


Subproblem 1
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 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 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {1.6, -1}

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