7x+x(x-7)=(2x+5)(5-2x)

Solution for 7x+x(x-7)=(2x+5)(5-2x) equation:

Simplifying
7x + x(x + -7) = (2x + 5)(5 + -2x)

Reorder the terms:
7x + x(-7 + x) = (2x + 5)(5 + -2x)
7x + (-7 * x + x * x) = (2x + 5)(5 + -2x)
7x + (-7x + x2) = (2x + 5)(5 + -2x)

Combine like terms: 7x + -7x = 0
0 + x2 = (2x + 5)(5 + -2x)
x2 = (2x + 5)(5 + -2x)

Reorder the terms:
x2 = (5 + 2x)(5 + -2x)

Multiply (5 + 2x) * (5 + -2x)
x2 = (5(5 + -2x) + 2x * (5 + -2x))
x2 = ((5 * 5 + -2x * 5) + 2x * (5 + -2x))
x2 = ((25 + -10x) + 2x * (5 + -2x))
x2 = (25 + -10x + (5 * 2x + -2x * 2x))
x2 = (25 + -10x + (10x + -4x2))

Combine like terms: -10x + 10x = 0
x2 = (25 + 0 + -4x2)
x2 = (25 + -4x2)

Solving
x2 = 25 + -4x2

Solving for variable 'x'.

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

Add '4x2' to each side of the equation.
x2 + 4x2 = 25 + -4x2 + 4x2

Combine like terms: x2 + 4x2 = 5x2
5x2 = 25 + -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
5x2 = 25 + 0
5x2 = 25

Divide each side by '5'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}