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

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


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

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

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

Multiply (1 + x) * (-3 + x)
(1(-3 + x) + x(-3 + x)) = (2x + 5)(x + -3)
((-3 * 1 + x * 1) + x(-3 + x)) = (2x + 5)(x + -3)
((-3 + 1x) + x(-3 + x)) = (2x + 5)(x + -3)
(-3 + 1x + (-3 * x + x * x)) = (2x + 5)(x + -3)
(-3 + 1x + (-3x + x2)) = (2x + 5)(x + -3)

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -3 + 15 = 12
12 + -2x + x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: -2x + x = -1x
12 + -1x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
12 + -1x + -1x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Reorder the terms:
12 + -1x + -1x2 = -15 + 15 + -1x + x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
12 + -1x + -1x2 = 0 + -1x + x + 2x2 + -2x2
12 + -1x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
12 + -1x + -1x2 = 0 + 2x2 + -2x2
12 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -1x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + x) = 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {3, -4}

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