3x^2+4x-5x+4=6

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


Simplifying
3x2 + 4x + -5x + 4 = 6

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

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

Solving
4 + -1x + 3x2 = 6

Solving for variable 'x'.

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

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

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

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

Subproblem 1

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

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 = {-0.6666666667, 1}

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