5x^2=3x+2

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


Simplifying
5x2 = 3x + 2

Reorder the terms:
5x2 = 2 + 3x

Solving
5x2 = 2 + 3x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(-2 + -5x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

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

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

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.4, 1}

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