x(5x+11)=2x^2-8x

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Solution for x(5x+11)=2x^2-8x equation:


Simplifying
x(5x + 11) = 2x2 + -8x

Reorder the terms:
x(11 + 5x) = 2x2 + -8x
(11 * x + 5x * x) = 2x2 + -8x
(11x + 5x2) = 2x2 + -8x

Reorder the terms:
11x + 5x2 = -8x + 2x2

Solving
11x + 5x2 = -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
11x + 8x + 5x2 + -2x2 = -8x + 2x2 + 8x + -2x2

Combine like terms: 11x + 8x = 19x
19x + 5x2 + -2x2 = -8x + 2x2 + 8x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
19x + 3x2 = -8x + 2x2 + 8x + -2x2

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(19 + 3x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(19 + 3x)' equal to zero and attempt to solve: Simplifying 19 + 3x = 0 Solving 19 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 3x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 3x = 0 + -19 3x = 0 + -19 Combine like terms: 0 + -19 = -19 3x = -19 Divide each side by '3'. x = -6.333333333 Simplifying x = -6.333333333

Solution

x = {0, -6.333333333}

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