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

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


Simplifying
2x2 + 2x + -4 = -1(x + 3)(x + 2)

Reorder the terms:
-4 + 2x + 2x2 = -1(x + 3)(x + 2)

Reorder the terms:
-4 + 2x + 2x2 = -1(3 + x)(x + 2)

Reorder the terms:
-4 + 2x + 2x2 = -1(3 + x)(2 + x)

Multiply (3 + x) * (2 + x)
-4 + 2x + 2x2 = -1(3(2 + x) + x(2 + x))
-4 + 2x + 2x2 = -1((2 * 3 + x * 3) + x(2 + x))
-4 + 2x + 2x2 = -1((6 + 3x) + x(2 + x))
-4 + 2x + 2x2 = -1(6 + 3x + (2 * x + x * x))
-4 + 2x + 2x2 = -1(6 + 3x + (2x + x2))

Combine like terms: 3x + 2x = 5x
-4 + 2x + 2x2 = -1(6 + 5x + x2)
-4 + 2x + 2x2 = (6 * -1 + 5x * -1 + x2 * -1)
-4 + 2x + 2x2 = (-6 + -5x + -1x2)

Solving
-4 + 2x + 2x2 = -6 + -5x + -1x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + 2x + 5x + 2x2 + x2 = -6 + -5x + -1x2 + 6 + 5x + x2

Combine like terms: -4 + 6 = 2
2 + 2x + 5x + 2x2 + x2 = -6 + -5x + -1x2 + 6 + 5x + x2

Combine like terms: 2x + 5x = 7x
2 + 7x + 2x2 + x2 = -6 + -5x + -1x2 + 6 + 5x + x2

Combine like terms: 2x2 + x2 = 3x2
2 + 7x + 3x2 = -6 + -5x + -1x2 + 6 + 5x + x2

Reorder the terms:
2 + 7x + 3x2 = -6 + 6 + -5x + 5x + -1x2 + x2

Combine like terms: -6 + 6 = 0
2 + 7x + 3x2 = 0 + -5x + 5x + -1x2 + x2
2 + 7x + 3x2 = -5x + 5x + -1x2 + x2

Combine like terms: -5x + 5x = 0
2 + 7x + 3x2 = 0 + -1x2 + x2
2 + 7x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
2 + 7x + 3x2 = 0

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

Subproblem 1

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

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 = {-2, -0.3333333333}

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