2x(x+2)-3(x^2-4)=0

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Solution for 2x(x+2)-3(x^2-4)=0 equation:


Simplifying
2x(x + 2) + -3(x2 + -4) = 0

Reorder the terms:
2x(2 + x) + -3(x2 + -4) = 0
(2 * 2x + x * 2x) + -3(x2 + -4) = 0
(4x + 2x2) + -3(x2 + -4) = 0

Reorder the terms:
4x + 2x2 + -3(-4 + x2) = 0
4x + 2x2 + (-4 * -3 + x2 * -3) = 0
4x + 2x2 + (12 + -3x2) = 0

Reorder the terms:
12 + 4x + 2x2 + -3x2 = 0

Combine like terms: 2x2 + -3x2 = -1x2
12 + 4x + -1x2 = 0

Solving
12 + 4x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {6, -2}

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