(x+6)(x-3)=(2x+5)(x-3)

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Solution for (x+6)(x-3)=(2x+5)(x-3) equation: 


Simplifying
(x + 6)(x + -3) = (2x + 5)(x + -3)

Reorder the terms:
(6 + x)(x + -3) = (2x + 5)(x + -3)

Reorder the terms:
(6 + x)(-3 + x) = (2x + 5)(x + -3)

Multiply (6 + x) * (-3 + x)
(6(-3 + x) + x(-3 + x)) = (2x + 5)(x + -3)
((-3 * 6 + x * 6) + x(-3 + x)) = (2x + 5)(x + -3)
((-18 + 6x) + x(-3 + x)) = (2x + 5)(x + -3)
(-18 + 6x + (-3 * x + x * x)) = (2x + 5)(x + -3)
(-18 + 6x + (-3x + x2)) = (2x + 5)(x + -3)

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

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

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

Multiply (5 + 2x) * (-3 + x)
-18 + 3x + x2 = (5(-3 + x) + 2x * (-3 + x))
-18 + 3x + x2 = ((-3 * 5 + x * 5) + 2x * (-3 + x))
-18 + 3x + x2 = ((-15 + 5x) + 2x * (-3 + x))
-18 + 3x + x2 = (-15 + 5x + (-3 * 2x + x * 2x))
-18 + 3x + x2 = (-15 + 5x + (-6x + 2x2))

Combine like terms: 5x + -6x = -1x
-18 + 3x + x2 = (-15 + -1x + 2x2)

Solving
-18 + 3x + x2 = -15 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 15 + 3x + x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: -18 + 15 = -3
-3 + 3x + x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: 3x + x = 4x
-3 + 4x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-3 + 4x + -1x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Reorder the terms:
-3 + 4x + -1x2 = -15 + 15 + -1x + x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
-3 + 4x + -1x2 = 0 + -1x + x + 2x2 + -2x2
-3 + 4x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
-3 + 4x + -1x2 = 0 + 2x2 + -2x2
-3 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3 + 4x + -1x2 = 0

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


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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}

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