11x=-3(2x^2+1)

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Solution for 11x=-3(2x^2+1) equation:


Simplifying
11x = -3(2x2 + 1)

Reorder the terms:
11x = -3(1 + 2x2)
11x = (1 * -3 + 2x2 * -3)
11x = (-3 + -6x2)

Solving
11x = -3 + -6x2

Solving for variable 'x'.

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

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

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

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

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

Subproblem 1

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

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 = {-1.5, -0.3333333333}

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