(3x^2+5x-2)-(2x^2-3x+7)=

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Solution for (3x^2+5x-2)-(2x^2-3x+7)= equation: 


Simplifying
(3x2 + 5x + -2) + -1(2x2 + -3x + 7) = 0

Reorder the terms:
(-2 + 5x + 3x2) + -1(2x2 + -3x + 7) = 0

Remove parenthesis around (-2 + 5x + 3x2)
-2 + 5x + 3x2 + -1(2x2 + -3x + 7) = 0

Reorder the terms:
-2 + 5x + 3x2 + -1(7 + -3x + 2x2) = 0
-2 + 5x + 3x2 + (7 * -1 + -3x * -1 + 2x2 * -1) = 0
-2 + 5x + 3x2 + (-7 + 3x + -2x2) = 0

Reorder the terms:
-2 + -7 + 5x + 3x + 3x2 + -2x2 = 0

Combine like terms: -2 + -7 = -9
-9 + 5x + 3x + 3x2 + -2x2 = 0

Combine like terms: 5x + 3x = 8x
-9 + 8x + 3x2 + -2x2 = 0

Combine like terms: 3x2 + -2x2 = 1x2
-9 + 8x + 1x2 = 0

Solving
-9 + 8x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 1}

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