6x^2-22x=-2x^2-3x-6

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Solution for 6x^2-22x=-2x^2-3x-6 equation:


Simplifying
6x2 + -22x = -2x2 + -3x + -6

Reorder the terms:
-22x + 6x2 = -2x2 + -3x + -6

Reorder the terms:
-22x + 6x2 = -6 + -3x + -2x2

Solving
-22x + 6x2 = -6 + -3x + -2x2

Solving for variable 'x'.

Reorder the terms:
6 + -22x + 3x + 6x2 + 2x2 = -6 + -3x + -2x2 + 6 + 3x + 2x2

Combine like terms: -22x + 3x = -19x
6 + -19x + 6x2 + 2x2 = -6 + -3x + -2x2 + 6 + 3x + 2x2

Combine like terms: 6x2 + 2x2 = 8x2
6 + -19x + 8x2 = -6 + -3x + -2x2 + 6 + 3x + 2x2

Reorder the terms:
6 + -19x + 8x2 = -6 + 6 + -3x + 3x + -2x2 + 2x2

Combine like terms: -6 + 6 = 0
6 + -19x + 8x2 = 0 + -3x + 3x + -2x2 + 2x2
6 + -19x + 8x2 = -3x + 3x + -2x2 + 2x2

Combine like terms: -3x + 3x = 0
6 + -19x + 8x2 = 0 + -2x2 + 2x2
6 + -19x + 8x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
6 + -19x + 8x2 = 0

Factor a trinomial.
(3 + -8x)(2 + -1x) = 0

Subproblem 1

Set the factor '(3 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {0.375, 2}

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