-(2x^2+4x-5)-(3x^2-3x+2)=x

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Solution for -(2x^2+4x-5)-(3x^2-3x+2)=x equation:


Simplifying
-1(2x2 + 4x + -5) + -1(3x2 + -3x + 2) = x

Reorder the terms:
-1(-5 + 4x + 2x2) + -1(3x2 + -3x + 2) = x
(-5 * -1 + 4x * -1 + 2x2 * -1) + -1(3x2 + -3x + 2) = x
(5 + -4x + -2x2) + -1(3x2 + -3x + 2) = x

Reorder the terms:
5 + -4x + -2x2 + -1(2 + -3x + 3x2) = x
5 + -4x + -2x2 + (2 * -1 + -3x * -1 + 3x2 * -1) = x
5 + -4x + -2x2 + (-2 + 3x + -3x2) = x

Reorder the terms:
5 + -2 + -4x + 3x + -2x2 + -3x2 = x

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

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

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

Solving
3 + -1x + -5x2 = x

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(3 + -5x)(1 + x) = 0


Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5x = 0 + -3

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

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

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0.6, -1}

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