10x^2=-12x-2

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Solution for 10x^2=-12x-2 equation:


Simplifying
10x2 = -12x + -2

Reorder the terms:
10x2 = -2 + -12x

Solving
10x2 = -2 + -12x

Solving for variable 'x'.

Reorder the terms:
2 + 12x + 10x2 = -2 + -12x + 2 + 12x

Reorder the terms:
2 + 12x + 10x2 = -2 + 2 + -12x + 12x

Combine like terms: -2 + 2 = 0
2 + 12x + 10x2 = 0 + -12x + 12x
2 + 12x + 10x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
2 + 12x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 6x + 5x2) = 0

Factor a trinomial.
2((1 + x)(1 + 5x)) = 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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2

Solution

x = {-1, -0.2}

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