3=2x^2+3x-2

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


Simplifying
3 = 2x2 + 3x + -2

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

Solving
3 = -2 + 3x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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


Subproblem 1
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

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

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1, -2.5}

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