x(5x+11)=2x^2-6x+6

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Solution for x(5x+11)=2x^2-6x+6 equation:


Simplifying
x(5x + 11) = 2x2 + -6x + 6

Reorder the terms:
x(11 + 5x) = 2x2 + -6x + 6
(11 * x + 5x * x) = 2x2 + -6x + 6
(11x + 5x2) = 2x2 + -6x + 6

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

Solving
11x + 5x2 = 6 + -6x + 2x2

Solving for variable 'x'.

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

Combine like terms: 11x + 6x = 17x
-6 + 17x + 5x2 + -2x2 = 6 + -6x + 2x2 + -6 + 6x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-6 + 17x + 3x2 = 6 + -6x + 2x2 + -6 + 6x + -2x2

Reorder the terms:
-6 + 17x + 3x2 = 6 + -6 + -6x + 6x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
-6 + 17x + 3x2 = 0 + -6x + 6x + 2x2 + -2x2
-6 + 17x + 3x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
-6 + 17x + 3x2 = 0 + 2x2 + -2x2
-6 + 17x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 17x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(1 + -3x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333

Solution

x = {-6, 0.3333333333}

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