(-x^2+5x-3)+(7x^2+4x+6)=

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Solution for (-x^2+5x-3)+(7x^2+4x+6)= equation:


Simplifying
(-1x2 + 5x + -3) + (7x2 + 4x + 6) = 0

Reorder the terms:
(-3 + 5x + -1x2) + (7x2 + 4x + 6) = 0

Remove parenthesis around (-3 + 5x + -1x2)
-3 + 5x + -1x2 + (7x2 + 4x + 6) = 0

Reorder the terms:
-3 + 5x + -1x2 + (6 + 4x + 7x2) = 0

Remove parenthesis around (6 + 4x + 7x2)
-3 + 5x + -1x2 + 6 + 4x + 7x2 = 0

Reorder the terms:
-3 + 6 + 5x + 4x + -1x2 + 7x2 = 0

Combine like terms: -3 + 6 = 3
3 + 5x + 4x + -1x2 + 7x2 = 0

Combine like terms: 5x + 4x = 9x
3 + 9x + -1x2 + 7x2 = 0

Combine like terms: -1x2 + 7x2 = 6x2
3 + 9x + 6x2 = 0

Solving
3 + 9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3x + 2x2) = 0

Factor a trinomial.
3((1 + x)(1 + 2x)) = 0

Ignore the factor 3.

Subproblem 1

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

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 = {-1, -0.5}

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