9x+1=3(x^2-5)-(x-3)(x+2)

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Solution for 9x+1=3(x^2-5)-(x-3)(x+2) equation: 


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

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

Reorder the terms:
1 + 9x = 3(-5 + x2) + -1(x + -3)(x + 2)
1 + 9x = (-5 * 3 + x2 * 3) + -1(x + -3)(x + 2)
1 + 9x = (-15 + 3x2) + -1(x + -3)(x + 2)

Reorder the terms:
1 + 9x = -15 + 3x2 + -1(-3 + x)(x + 2)

Reorder the terms:
1 + 9x = -15 + 3x2 + -1(-3 + x)(2 + x)

Multiply (-3 + x) * (2 + x)
1 + 9x = -15 + 3x2 + -1(-3(2 + x) + x(2 + x))
1 + 9x = -15 + 3x2 + -1((2 * -3 + x * -3) + x(2 + x))
1 + 9x = -15 + 3x2 + -1((-6 + -3x) + x(2 + x))
1 + 9x = -15 + 3x2 + -1(-6 + -3x + (2 * x + x * x))
1 + 9x = -15 + 3x2 + -1(-6 + -3x + (2x + x2))

Combine like terms: -3x + 2x = -1x
1 + 9x = -15 + 3x2 + -1(-6 + -1x + x2)
1 + 9x = -15 + 3x2 + (-6 * -1 + -1x * -1 + x2 * -1)
1 + 9x = -15 + 3x2 + (6 + 1x + -1x2)

Reorder the terms:
1 + 9x = -15 + 6 + 1x + 3x2 + -1x2

Combine like terms: -15 + 6 = -9
1 + 9x = -9 + 1x + 3x2 + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
1 + 9x = -9 + 1x + 2x2

Solving
1 + 9x = -9 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 9 + 9x + -1x + -2x2 = -9 + 1x + 2x2 + 9 + -1x + -2x2

Combine like terms: 1 + 9 = 10
10 + 9x + -1x + -2x2 = -9 + 1x + 2x2 + 9 + -1x + -2x2

Combine like terms: 9x + -1x = 8x
10 + 8x + -2x2 = -9 + 1x + 2x2 + 9 + -1x + -2x2

Reorder the terms:
10 + 8x + -2x2 = -9 + 9 + 1x + -1x + 2x2 + -2x2

Combine like terms: -9 + 9 = 0
10 + 8x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
10 + 8x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
10 + 8x + -2x2 = 0 + 2x2 + -2x2
10 + 8x + -2x2 = 2x2 + -2x2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, -1}

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