2x^2-13x=-3x^2-2x-6

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Solution for 2x^2-13x=-3x^2-2x-6 equation:


Simplifying
2x2 + -13x = -3x2 + -2x + -6

Reorder the terms:
-13x + 2x2 = -3x2 + -2x + -6

Reorder the terms:
-13x + 2x2 = -6 + -2x + -3x2

Solving
-13x + 2x2 = -6 + -2x + -3x2

Solving for variable 'x'.

Reorder the terms:
6 + -13x + 2x + 2x2 + 3x2 = -6 + -2x + -3x2 + 6 + 2x + 3x2

Combine like terms: -13x + 2x = -11x
6 + -11x + 2x2 + 3x2 = -6 + -2x + -3x2 + 6 + 2x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
6 + -11x + 5x2 = -6 + -2x + -3x2 + 6 + 2x + 3x2

Reorder the terms:
6 + -11x + 5x2 = -6 + 6 + -2x + 2x + -3x2 + 3x2

Combine like terms: -6 + 6 = 0
6 + -11x + 5x2 = 0 + -2x + 2x + -3x2 + 3x2
6 + -11x + 5x2 = -2x + 2x + -3x2 + 3x2

Combine like terms: -2x + 2x = 0
6 + -11x + 5x2 = 0 + -3x2 + 3x2
6 + -11x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
6 + -11x + 5x2 = 0

Factor a trinomial.
(1 + -1x)(6 + -5x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 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 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2

Solution

x = {1, 1.2}

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