(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 = -1x
-6 + -1x + 6x + 2x2 + 4x2 = 0

Combine like terms: -1x + 6x = 5x
-6 + 5x + 2x2 + 4x2 = 0

Combine like terms: 2x2 + 4x2 = 6x2
-6 + 5x + 6x2 = 0

Solving
-6 + 5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x)(2 + -3x) = 0

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667

Solution

x = {-1.5, 0.6666666667}

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