x^2-9=(x-3)(4x+6)

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Solution for x^2-9=(x-3)(4x+6) equation: 


Simplifying
x2 + -9 = (x + -3)(4x + 6)

Reorder the terms:
-9 + x2 = (x + -3)(4x + 6)

Reorder the terms:
-9 + x2 = (-3 + x)(4x + 6)

Reorder the terms:
-9 + x2 = (-3 + x)(6 + 4x)

Multiply (-3 + x) * (6 + 4x)
-9 + x2 = (-3(6 + 4x) + x(6 + 4x))
-9 + x2 = ((6 * -3 + 4x * -3) + x(6 + 4x))
-9 + x2 = ((-18 + -12x) + x(6 + 4x))
-9 + x2 = (-18 + -12x + (6 * x + 4x * x))
-9 + x2 = (-18 + -12x + (6x + 4x2))

Combine like terms: -12x + 6x = -6x
-9 + x2 = (-18 + -6x + 4x2)

Solving
-9 + x2 = -18 + -6x + 4x2

Solving for variable 'x'.

Reorder the terms:
-9 + 18 + 6x + x2 + -4x2 = -18 + -6x + 4x2 + 18 + 6x + -4x2

Combine like terms: -9 + 18 = 9
9 + 6x + x2 + -4x2 = -18 + -6x + 4x2 + 18 + 6x + -4x2

Combine like terms: x2 + -4x2 = -3x2
9 + 6x + -3x2 = -18 + -6x + 4x2 + 18 + 6x + -4x2

Reorder the terms:
9 + 6x + -3x2 = -18 + 18 + -6x + 6x + 4x2 + -4x2

Combine like terms: -18 + 18 = 0
9 + 6x + -3x2 = 0 + -6x + 6x + 4x2 + -4x2
9 + 6x + -3x2 = -6x + 6x + 4x2 + -4x2

Combine like terms: -6x + 6x = 0
9 + 6x + -3x2 = 0 + 4x2 + -4x2
9 + 6x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + 6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 2x + -1x2) = 0

Factor a trinomial.
3((3 + -1x)(1 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, -1}

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