(2x^2+3x-2)+(4x+3)+(-4x^2+6x-7)=0

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Solution for (2x^2+3x-2)+(4x+3)+(-4x^2+6x-7)=0 equation: 


Simplifying
(2x2 + 3x + -2) + (4x + 3) + (-4x2 + 6x + -7) = 0

Reorder the terms:
(-2 + 3x + 2x2) + (4x + 3) + (-4x2 + 6x + -7) = 0

Remove parenthesis around (-2 + 3x + 2x2)
-2 + 3x + 2x2 + (4x + 3) + (-4x2 + 6x + -7) = 0

Reorder the terms:
-2 + 3x + 2x2 + (3 + 4x) + (-4x2 + 6x + -7) = 0

Remove parenthesis around (3 + 4x)
-2 + 3x + 2x2 + 3 + 4x + (-4x2 + 6x + -7) = 0

Reorder the terms:
-2 + 3x + 2x2 + 3 + 4x + (-7 + 6x + -4x2) = 0

Remove parenthesis around (-7 + 6x + -4x2)
-2 + 3x + 2x2 + 3 + 4x + -7 + 6x + -4x2 = 0

Reorder the terms:
-2 + 3 + -7 + 3x + 4x + 6x + 2x2 + -4x2 = 0

Combine like terms: -2 + 3 = 1
1 + -7 + 3x + 4x + 6x + 2x2 + -4x2 = 0

Combine like terms: 1 + -7 = -6
-6 + 3x + 4x + 6x + 2x2 + -4x2 = 0

Combine like terms: 3x + 4x = 7x
-6 + 7x + 6x + 2x2 + -4x2 = 0

Combine like terms: 7x + 6x = 13x
-6 + 13x + 2x2 + -4x2 = 0

Combine like terms: 2x2 + -4x2 = -2x2
-6 + 13x + -2x2 = 0

Solving
-6 + 13x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(1 + -2x) = 0


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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {6, 0.5}

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