(x-3)(x+5)=x^2+gx-15

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Solution for (x-3)(x+5)=x^2+gx-15 equation: 


Simplifying
(x + -3)(x + 5) = x2 + gx + -15

Reorder the terms:
(-3 + x)(x + 5) = x2 + gx + -15

Reorder the terms:
(-3 + x)(5 + x) = x2 + gx + -15

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) = x2 + gx + -15
((5 * -3 + x * -3) + x(5 + x)) = x2 + gx + -15
((-15 + -3x) + x(5 + x)) = x2 + gx + -15
(-15 + -3x + (5 * x + x * x)) = x2 + gx + -15
(-15 + -3x + (5x + x2)) = x2 + gx + -15

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) = x2 + gx + -15

Reorder the terms:
-15 + 2x + x2 = -15 + gx + x2

Add '15' to each side of the equation.
-15 + 2x + 15 + x2 = -15 + gx + 15 + x2

Reorder the terms:
-15 + 15 + 2x + x2 = -15 + gx + 15 + x2

Combine like terms: -15 + 15 = 0
0 + 2x + x2 = -15 + gx + 15 + x2
2x + x2 = -15 + gx + 15 + x2

Reorder the terms:
2x + x2 = -15 + 15 + gx + x2

Combine like terms: -15 + 15 = 0
2x + x2 = 0 + gx + x2
2x + x2 = gx + x2

Add '-1x2' to each side of the equation.
2x + x2 + -1x2 = gx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2x + 0 = gx + x2 + -1x2
2x = gx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2x = gx + 0
2x = gx

Solving
2x = gx

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1gx' to each side of the equation.
-1gx + 2x = gx + -1gx

Combine like terms: gx + -1gx = 0
-1gx + 2x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1g + 2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-1g + 2)' equal to zero and attempt to solve:

Simplifying
-1g + 2 = 0

Reorder the terms:
2 + -1g = 0

Solving
2 + -1g = 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 + -1g = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g = 0 + -2
-1g = 0 + -2

Combine like terms: 0 + -2 = -2
-1g = -2

Add 'g' to each side of the equation.
-1g + g = -2 + g

Combine like terms: -1g + g = 0
0 = -2 + g

Simplifying
0 = -2 + g

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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