(x-7)*(x-3)+10x=30

Solution for (x-7)*(x-3)+10x=30 equation:

Simplifying
(x + -7)(x + -3) + 10x = 30

Reorder the terms:
(-7 + x)(x + -3) + 10x = 30

Reorder the terms:
(-7 + x)(-3 + x) + 10x = 30

Multiply (-7 + x) * (-3 + x)
(-7(-3 + x) + x(-3 + x)) + 10x = 30
((-3 * -7 + x * -7) + x(-3 + x)) + 10x = 30
((21 + -7x) + x(-3 + x)) + 10x = 30
(21 + -7x + (-3 * x + x * x)) + 10x = 30
(21 + -7x + (-3x + x2)) + 10x = 30

Combine like terms: -7x + -3x = -10x
(21 + -10x + x2) + 10x = 30

Reorder the terms:
21 + -10x + 10x + x2 = 30

Combine like terms: -10x + 10x = 0
21 + 0 + x2 = 30
21 + x2 = 30

Solving
21 + x2 = 30

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x2 = 30 + -21

Combine like terms: 21 + -21 = 0
0 + x2 = 30 + -21
x2 = 30 + -21

Combine like terms: 30 + -21 = 9
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}