4x(x+1)=75+x(x+4)

Solution for 4x(x+1)=75+x(x+4) equation:

Simplifying
4x(x + 1) = 75 + x(x + 4)

Reorder the terms:
4x(1 + x) = 75 + x(x + 4)
(1 * 4x + x * 4x) = 75 + x(x + 4)
(4x + 4x2) = 75 + x(x + 4)

Reorder the terms:
4x + 4x2 = 75 + x(4 + x)
4x + 4x2 = 75 + (4 * x + x * x)
4x + 4x2 = 75 + (4x + x2)

Add '-4x' to each side of the equation.
4x + -4x + 4x2 = 75 + 4x + -4x + x2

Combine like terms: 4x + -4x = 0
0 + 4x2 = 75 + 4x + -4x + x2
4x2 = 75 + 4x + -4x + x2

Combine like terms: 4x + -4x = 0
4x2 = 75 + 0 + x2
4x2 = 75 + x2

Solving
4x2 = 75 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
4x2 + -1x2 = 75 + x2 + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
3x2 = 75 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x2 = 75 + 0
3x2 = 75

Divide each side by '3'.
x2 = 25

Simplifying
x2 = 25

Take the square root of each side:
x = {-5, 5}