10x^2=-24x-8

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Solution for 10x^2=-24x-8 equation:


Simplifying
10x2 = -24x + -8

Reorder the terms:
10x2 = -8 + -24x

Solving
10x2 = -8 + -24x

Solving for variable 'x'.

Reorder the terms:
8 + 24x + 10x2 = -8 + -24x + 8 + 24x

Reorder the terms:
8 + 24x + 10x2 = -8 + 8 + -24x + 24x

Combine like terms: -8 + 8 = 0
8 + 24x + 10x2 = 0 + -24x + 24x
8 + 24x + 10x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
8 + 24x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12x + 5x2) = 0

Factor a trinomial.
2((2 + x)(2 + 5x)) = 0

Ignore the factor 2.

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 '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 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 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4

Solution

x = {-2, -0.4}

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