8x^2=-28x-24

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Solution for 8x^2=-28x-24 equation:


Simplifying
8x2 = -28x + -24

Reorder the terms:
8x2 = -24 + -28x

Solving
8x2 = -24 + -28x

Solving for variable 'x'.

Reorder the terms:
24 + 28x + 8x2 = -24 + -28x + 24 + 28x

Reorder the terms:
24 + 28x + 8x2 = -24 + 24 + -28x + 28x

Combine like terms: -24 + 24 = 0
24 + 28x + 8x2 = 0 + -28x + 28x
24 + 28x + 8x2 = -28x + 28x

Combine like terms: -28x + 28x = 0
24 + 28x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 7x + 2x2) = 0

Factor a trinomial.
4((2 + x)(3 + 2x)) = 0

Ignore the factor 4.

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 '(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

Solution

x = {-2, -1.5}

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