(x^2-5x+7)-(2x^2+3x-2)=0

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Solution for (x^2-5x+7)-(2x^2+3x-2)=0 equation: 


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

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

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

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

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

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

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

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

Solving
9 + -8x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(9 + x) = 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 '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {1, -9}

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