(3x^2-5x+1)-(2x-3)=

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Solution for (3x^2-5x+1)-(2x-3)= equation: 


Simplifying
(3x2 + -5x + 1) + -1(2x + -3) = 0

Reorder the terms:
(1 + -5x + 3x2) + -1(2x + -3) = 0

Remove parenthesis around (1 + -5x + 3x2)
1 + -5x + 3x2 + -1(2x + -3) = 0

Reorder the terms:
1 + -5x + 3x2 + -1(-3 + 2x) = 0
1 + -5x + 3x2 + (-3 * -1 + 2x * -1) = 0
1 + -5x + 3x2 + (3 + -2x) = 0

Reorder the terms:
1 + 3 + -5x + -2x + 3x2 = 0

Combine like terms: 1 + 3 = 4
4 + -5x + -2x + 3x2 = 0

Combine like terms: -5x + -2x = -7x
4 + -7x + 3x2 = 0

Solving
4 + -7x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(4 + -3x) = 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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {1, 1.333333333}

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