6(x-5)-15(x-7)=-3x^2+6-105

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Solution for 6(x-5)-15(x-7)=-3x^2+6-105 equation:


Simplifying
6(x + -5) + -15(x + -7) = -3x2 + 6 + -105

Reorder the terms:
6(-5 + x) + -15(x + -7) = -3x2 + 6 + -105
(-5 * 6 + x * 6) + -15(x + -7) = -3x2 + 6 + -105
(-30 + 6x) + -15(x + -7) = -3x2 + 6 + -105

Reorder the terms:
-30 + 6x + -15(-7 + x) = -3x2 + 6 + -105
-30 + 6x + (-7 * -15 + x * -15) = -3x2 + 6 + -105
-30 + 6x + (105 + -15x) = -3x2 + 6 + -105

Reorder the terms:
-30 + 105 + 6x + -15x = -3x2 + 6 + -105

Combine like terms: -30 + 105 = 75
75 + 6x + -15x = -3x2 + 6 + -105

Combine like terms: 6x + -15x = -9x
75 + -9x = -3x2 + 6 + -105

Reorder the terms:
75 + -9x = 6 + -105 + -3x2

Combine like terms: 6 + -105 = -99
75 + -9x = -99 + -3x2

Solving
75 + -9x = -99 + -3x2

Solving for variable 'x'.

Reorder the terms:
75 + 99 + -9x + 3x2 = -99 + -3x2 + 99 + 3x2

Combine like terms: 75 + 99 = 174
174 + -9x + 3x2 = -99 + -3x2 + 99 + 3x2

Reorder the terms:
174 + -9x + 3x2 = -99 + 99 + -3x2 + 3x2

Combine like terms: -99 + 99 = 0
174 + -9x + 3x2 = 0 + -3x2 + 3x2
174 + -9x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
174 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(58 + -3x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(58 + -3x + x2)' equal to zero and attempt to solve: Simplifying 58 + -3x + x2 = 0 Solving 58 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + -3x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + -3x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + -3x + x2 = 0 + -58 -3x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 -3x + x2 = -58 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -58 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -58 + 2.25 Combine like terms: -58 + 2.25 = -55.75 2.25 + -3x + x2 = -55.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -55.75 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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