(x+6)(x-3)=(2x+1)(x-3)

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Solution for (x+6)(x-3)=(2x+1)(x-3) equation: 


Simplifying
(x + 6)(x + -3) = (2x + 1)(x + -3)

Reorder the terms:
(6 + x)(x + -3) = (2x + 1)(x + -3)

Reorder the terms:
(6 + x)(-3 + x) = (2x + 1)(x + -3)

Multiply (6 + x) * (-3 + x)
(6(-3 + x) + x(-3 + x)) = (2x + 1)(x + -3)
((-3 * 6 + x * 6) + x(-3 + x)) = (2x + 1)(x + -3)
((-18 + 6x) + x(-3 + x)) = (2x + 1)(x + -3)
(-18 + 6x + (-3 * x + x * x)) = (2x + 1)(x + -3)
(-18 + 6x + (-3x + x2)) = (2x + 1)(x + -3)

Combine like terms: 6x + -3x = 3x
(-18 + 3x + x2) = (2x + 1)(x + -3)

Reorder the terms:
-18 + 3x + x2 = (1 + 2x)(x + -3)

Reorder the terms:
-18 + 3x + x2 = (1 + 2x)(-3 + x)

Multiply (1 + 2x) * (-3 + x)
-18 + 3x + x2 = (1(-3 + x) + 2x * (-3 + x))
-18 + 3x + x2 = ((-3 * 1 + x * 1) + 2x * (-3 + x))
-18 + 3x + x2 = ((-3 + 1x) + 2x * (-3 + x))
-18 + 3x + x2 = (-3 + 1x + (-3 * 2x + x * 2x))
-18 + 3x + x2 = (-3 + 1x + (-6x + 2x2))

Combine like terms: 1x + -6x = -5x
-18 + 3x + x2 = (-3 + -5x + 2x2)

Solving
-18 + 3x + x2 = -3 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 3 + 3x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2

Combine like terms: -18 + 3 = -15
-15 + 3x + 5x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2

Combine like terms: 3x + 5x = 8x
-15 + 8x + x2 + -2x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-15 + 8x + -1x2 = -3 + -5x + 2x2 + 3 + 5x + -2x2

Reorder the terms:
-15 + 8x + -1x2 = -3 + 3 + -5x + 5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
-15 + 8x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2
-15 + 8x + -1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-15 + 8x + -1x2 = 0 + 2x2 + -2x2
-15 + 8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 8x + -1x2 = 0

Factor a trinomial.
(-5 + x)(3 + -1x) = 0


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

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 3}

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