(x-6)(x+3)=5(x+3)

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Solution for (x-6)(x+3)=5(x+3) equation:


Simplifying
(x + -6)(x + 3) = 5(x + 3)

Reorder the terms:
(-6 + x)(x + 3) = 5(x + 3)

Reorder the terms:
(-6 + x)(3 + x) = 5(x + 3)

Multiply (-6 + x) * (3 + x)
(-6(3 + x) + x(3 + x)) = 5(x + 3)
((3 * -6 + x * -6) + x(3 + x)) = 5(x + 3)
((-18 + -6x) + x(3 + x)) = 5(x + 3)
(-18 + -6x + (3 * x + x * x)) = 5(x + 3)
(-18 + -6x + (3x + x2)) = 5(x + 3)

Combine like terms: -6x + 3x = -3x
(-18 + -3x + x2) = 5(x + 3)

Reorder the terms:
-18 + -3x + x2 = 5(3 + x)
-18 + -3x + x2 = (3 * 5 + x * 5)
-18 + -3x + x2 = (15 + 5x)

Solving
-18 + -3x + x2 = 15 + 5x

Solving for variable 'x'.

Reorder the terms:
-18 + -15 + -3x + -5x + x2 = 15 + 5x + -15 + -5x

Combine like terms: -18 + -15 = -33
-33 + -3x + -5x + x2 = 15 + 5x + -15 + -5x

Combine like terms: -3x + -5x = -8x
-33 + -8x + x2 = 15 + 5x + -15 + -5x

Reorder the terms:
-33 + -8x + x2 = 15 + -15 + 5x + -5x

Combine like terms: 15 + -15 = 0
-33 + -8x + x2 = 0 + 5x + -5x
-33 + -8x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-33 + -8x + x2 = 0

Factor a trinomial.
(-3 + -1x)(11 + -1x) = 0


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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-3, 11}

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