4x(x+1)=(2x+3)(x-5)

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Solution for 4x(x+1)=(2x+3)(x-5) equation: 


Simplifying
4x(x + 1) = (2x + 3)(x + -5)

Reorder the terms:
4x(1 + x) = (2x + 3)(x + -5)
(1 * 4x + x * 4x) = (2x + 3)(x + -5)
(4x + 4x2) = (2x + 3)(x + -5)

Reorder the terms:
4x + 4x2 = (3 + 2x)(x + -5)

Reorder the terms:
4x + 4x2 = (3 + 2x)(-5 + x)

Multiply (3 + 2x) * (-5 + x)
4x + 4x2 = (3(-5 + x) + 2x * (-5 + x))
4x + 4x2 = ((-5 * 3 + x * 3) + 2x * (-5 + x))
4x + 4x2 = ((-15 + 3x) + 2x * (-5 + x))
4x + 4x2 = (-15 + 3x + (-5 * 2x + x * 2x))
4x + 4x2 = (-15 + 3x + (-10x + 2x2))

Combine like terms: 3x + -10x = -7x
4x + 4x2 = (-15 + -7x + 2x2)

Solving
4x + 4x2 = -15 + -7x + 2x2

Solving for variable 'x'.

Reorder the terms:
15 + 4x + 7x + 4x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Combine like terms: 4x + 7x = 11x
15 + 11x + 4x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
15 + 11x + 2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Reorder the terms:
15 + 11x + 2x2 = -15 + 15 + -7x + 7x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
15 + 11x + 2x2 = 0 + -7x + 7x + 2x2 + -2x2
15 + 11x + 2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
15 + 11x + 2x2 = 0 + 2x2 + -2x2
15 + 11x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + 11x + 2x2 = 0

Factor a trinomial.
(3 + x)(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-3, -2.5}

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