(3x^2+4x-2)+(2x^2-3x-4)=0

Solution for (3x^2+4x-2)+(2x^2-3x-4)=0 equation:

Simplifying
(3x2 + 4x + -2) + (2x2 + -3x + -4) = 0

Reorder the terms:
(-2 + 4x + 3x2) + (2x2 + -3x + -4) = 0

Remove parenthesis around (-2 + 4x + 3x2)
-2 + 4x + 3x2 + (2x2 + -3x + -4) = 0

Reorder the terms:
-2 + 4x + 3x2 + (-4 + -3x + 2x2) = 0

Remove parenthesis around (-4 + -3x + 2x2)
-2 + 4x + 3x2 + -4 + -3x + 2x2 = 0

Reorder the terms:
-2 + -4 + 4x + -3x + 3x2 + 2x2 = 0

Combine like terms: -2 + -4 = -6
-6 + 4x + -3x + 3x2 + 2x2 = 0

Combine like terms: 4x + -3x = 1x
-6 + 1x + 3x2 + 2x2 = 0

Combine like terms: 3x2 + 2x2 = 5x2
-6 + 1x + 5x2 = 0

Solving
-6 + 1x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -5x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2
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 = {-1.2, 1}