5x(x+1)=(4x-7)(x+1)

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Solution for 5x(x+1)=(4x-7)(x+1) equation: 


Simplifying
5x(x + 1) = (4x + -7)(x + 1)

Reorder the terms:
5x(1 + x) = (4x + -7)(x + 1)
(1 * 5x + x * 5x) = (4x + -7)(x + 1)
(5x + 5x2) = (4x + -7)(x + 1)

Reorder the terms:
5x + 5x2 = (-7 + 4x)(x + 1)

Reorder the terms:
5x + 5x2 = (-7 + 4x)(1 + x)

Multiply (-7 + 4x) * (1 + x)
5x + 5x2 = (-7(1 + x) + 4x * (1 + x))
5x + 5x2 = ((1 * -7 + x * -7) + 4x * (1 + x))
5x + 5x2 = ((-7 + -7x) + 4x * (1 + x))
5x + 5x2 = (-7 + -7x + (1 * 4x + x * 4x))
5x + 5x2 = (-7 + -7x + (4x + 4x2))

Combine like terms: -7x + 4x = -3x
5x + 5x2 = (-7 + -3x + 4x2)

Solving
5x + 5x2 = -7 + -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
7 + 5x + 3x + 5x2 + -4x2 = -7 + -3x + 4x2 + 7 + 3x + -4x2

Combine like terms: 5x + 3x = 8x
7 + 8x + 5x2 + -4x2 = -7 + -3x + 4x2 + 7 + 3x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
7 + 8x + 1x2 = -7 + -3x + 4x2 + 7 + 3x + -4x2

Reorder the terms:
7 + 8x + 1x2 = -7 + 7 + -3x + 3x + 4x2 + -4x2

Combine like terms: -7 + 7 = 0
7 + 8x + 1x2 = 0 + -3x + 3x + 4x2 + -4x2
7 + 8x + 1x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
7 + 8x + 1x2 = 0 + 4x2 + -4x2
7 + 8x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
7 + 8x + 1x2 = 0

Factor a trinomial.
(7 + x)(1 + x) = 0


Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-7, -1}

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