3x(2x+2)-2x^2+2=0

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Solution for 3x(2x+2)-2x^2+2=0 equation:


Simplifying
3x(2x + 2) + -2x2 + 2 = 0

Reorder the terms:
3x(2 + 2x) + -2x2 + 2 = 0
(2 * 3x + 2x * 3x) + -2x2 + 2 = 0
(6x + 6x2) + -2x2 + 2 = 0

Reorder the terms:
2 + 6x + 6x2 + -2x2 = 0

Combine like terms: 6x2 + -2x2 = 4x2
2 + 6x + 4x2 = 0

Solving
2 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-1, -0.5}

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