(3x^2-5x^2+8x-2)-(3x^2-9x^2+2x-12)=0

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Solution for (3x^2-5x^2+8x-2)-(3x^2-9x^2+2x-12)=0 equation:


Simplifying
(3x2 + -5x2 + 8x + -2) + -1(3x2 + -9x2 + 2x + -12) = 0

Reorder the terms:
(-2 + 8x + 3x2 + -5x2) + -1(3x2 + -9x2 + 2x + -12) = 0

Combine like terms: 3x2 + -5x2 = -2x2
(-2 + 8x + -2x2) + -1(3x2 + -9x2 + 2x + -12) = 0

Remove parenthesis around (-2 + 8x + -2x2)
-2 + 8x + -2x2 + -1(3x2 + -9x2 + 2x + -12) = 0

Reorder the terms:
-2 + 8x + -2x2 + -1(-12 + 2x + 3x2 + -9x2) = 0

Combine like terms: 3x2 + -9x2 = -6x2
-2 + 8x + -2x2 + -1(-12 + 2x + -6x2) = 0
-2 + 8x + -2x2 + (-12 * -1 + 2x * -1 + -6x2 * -1) = 0
-2 + 8x + -2x2 + (12 + -2x + 6x2) = 0

Reorder the terms:
-2 + 12 + 8x + -2x + -2x2 + 6x2 = 0

Combine like terms: -2 + 12 = 10
10 + 8x + -2x + -2x2 + 6x2 = 0

Combine like terms: 8x + -2x = 6x
10 + 6x + -2x2 + 6x2 = 0

Combine like terms: -2x2 + 6x2 = 4x2
10 + 6x + 4x2 = 0

Solving
10 + 6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 3x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 2x2 = 0 Solving 5 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 1.5x + x2 = 0 + -2.5 1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 1.5x + x2 = -2.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + 1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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