4x(x+7)=(3x-1)(x+7)

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Solution for 4x(x+7)=(3x-1)(x+7) equation: 


Simplifying
4x(x + 7) = (3x + -1)(x + 7)

Reorder the terms:
4x(7 + x) = (3x + -1)(x + 7)
(7 * 4x + x * 4x) = (3x + -1)(x + 7)
(28x + 4x2) = (3x + -1)(x + 7)

Reorder the terms:
28x + 4x2 = (-1 + 3x)(x + 7)

Reorder the terms:
28x + 4x2 = (-1 + 3x)(7 + x)

Multiply (-1 + 3x) * (7 + x)
28x + 4x2 = (-1(7 + x) + 3x * (7 + x))
28x + 4x2 = ((7 * -1 + x * -1) + 3x * (7 + x))
28x + 4x2 = ((-7 + -1x) + 3x * (7 + x))
28x + 4x2 = (-7 + -1x + (7 * 3x + x * 3x))
28x + 4x2 = (-7 + -1x + (21x + 3x2))

Combine like terms: -1x + 21x = 20x
28x + 4x2 = (-7 + 20x + 3x2)

Solving
28x + 4x2 = -7 + 20x + 3x2

Solving for variable 'x'.

Reorder the terms:
7 + 28x + -20x + 4x2 + -3x2 = -7 + 20x + 3x2 + 7 + -20x + -3x2

Combine like terms: 28x + -20x = 8x
7 + 8x + 4x2 + -3x2 = -7 + 20x + 3x2 + 7 + -20x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
7 + 8x + 1x2 = -7 + 20x + 3x2 + 7 + -20x + -3x2

Reorder the terms:
7 + 8x + 1x2 = -7 + 7 + 20x + -20x + 3x2 + -3x2

Combine like terms: -7 + 7 = 0
7 + 8x + 1x2 = 0 + 20x + -20x + 3x2 + -3x2
7 + 8x + 1x2 = 20x + -20x + 3x2 + -3x2

Combine like terms: 20x + -20x = 0
7 + 8x + 1x2 = 0 + 3x2 + -3x2
7 + 8x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 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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