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

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

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

Multiply x * x
x2 + (x + 1)(x + 1) = (2x + -1)(x + 4)

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

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

Multiply (1 + x) * (1 + x)
x2 + (1(1 + x) + x(1 + x)) = (2x + -1)(x + 4)
x2 + ((1 * 1 + x * 1) + x(1 + x)) = (2x + -1)(x + 4)
x2 + ((1 + 1x) + x(1 + x)) = (2x + -1)(x + 4)
x2 + (1 + 1x + (1 * x + x * x)) = (2x + -1)(x + 4)
x2 + (1 + 1x + (1x + x2)) = (2x + -1)(x + 4)

Combine like terms: 1x + 1x = 2x
x2 + (1 + 2x + x2) = (2x + -1)(x + 4)

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

Combine like terms: x2 + x2 = 2x2
1 + 2x + 2x2 = (2x + -1)(x + 4)

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

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

Multiply (-1 + 2x) * (4 + x)
1 + 2x + 2x2 = (-1(4 + x) + 2x * (4 + x))
1 + 2x + 2x2 = ((4 * -1 + x * -1) + 2x * (4 + x))
1 + 2x + 2x2 = ((-4 + -1x) + 2x * (4 + x))
1 + 2x + 2x2 = (-4 + -1x + (4 * 2x + x * 2x))
1 + 2x + 2x2 = (-4 + -1x + (8x + 2x2))

Combine like terms: -1x + 8x = 7x
1 + 2x + 2x2 = (-4 + 7x + 2x2)

Add '-2x2' to each side of the equation.
1 + 2x + 2x2 + -2x2 = -4 + 7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + 2x + 0 = -4 + 7x + 2x2 + -2x2
1 + 2x = -4 + 7x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + 2x = -4 + 7x + 0
1 + 2x = -4 + 7x

Solving
1 + 2x = -4 + 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.
1 + 2x + -7x = -4 + 7x + -7x

Combine like terms: 2x + -7x = -5x
1 + -5x = -4 + 7x + -7x

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

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

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

Combine like terms: -4 + -1 = -5
-5x = -5

Divide each side by '-5'.
x = 1

Simplifying
x = 1