10x^2+60x+50=-25-2x^2

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Solution for 10x^2+60x+50=-25-2x^2 equation:


Simplifying
10x2 + 60x + 50 = -25 + -2x2

Reorder the terms:
50 + 60x + 10x2 = -25 + -2x2

Solving
50 + 60x + 10x2 = -25 + -2x2

Solving for variable 'x'.

Reorder the terms:
50 + 25 + 60x + 10x2 + 2x2 = -25 + -2x2 + 25 + 2x2

Combine like terms: 50 + 25 = 75
75 + 60x + 10x2 + 2x2 = -25 + -2x2 + 25 + 2x2

Combine like terms: 10x2 + 2x2 = 12x2
75 + 60x + 12x2 = -25 + -2x2 + 25 + 2x2

Reorder the terms:
75 + 60x + 12x2 = -25 + 25 + -2x2 + 2x2

Combine like terms: -25 + 25 = 0
75 + 60x + 12x2 = 0 + -2x2 + 2x2
75 + 60x + 12x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
75 + 60x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 20x + 4x2) = 0

Factor a trinomial.
3((5 + 2x)(5 + 2x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

Solution

x = {-2.5, -2.5}

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