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

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


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

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

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

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

Combine like terms: 1x + 4x = 5x
(4 + 5x + x2) = x(x + 7)

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

Add '-1x2' to each side of the equation.
4 + 5x + x2 + -1x2 = 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 5x + 0 = 7x + x2 + -1x2
4 + 5x = 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + 5x = 7x + 0
4 + 5x = 7x

Solving
4 + 5x = 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
4 + 5x + -7x = 7x + -7x

Combine like terms: 5x + -7x = -2x
4 + -2x = 7x + -7x

Combine like terms: 7x + -7x = 0
4 + -2x = 0

Add '-4' to each side of the equation.
4 + -4 + -2x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -2x = 0 + -4
-2x = 0 + -4

Combine like terms: 0 + -4 = -4
-2x = -4

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

Simplifying
x = 2

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