(x-3)(x-2)=7x-30

Solution for (x-3)(x-2)=7x-30 equation:

Simplifying
(x + -3)(x + -2) = 7x + -30

Reorder the terms:
(-3 + x)(x + -2) = 7x + -30

Reorder the terms:
(-3 + x)(-2 + x) = 7x + -30

Multiply (-3 + x) * (-2 + x)
(-3(-2 + x) + x(-2 + x)) = 7x + -30
((-2 * -3 + x * -3) + x(-2 + x)) = 7x + -30
((6 + -3x) + x(-2 + x)) = 7x + -30
(6 + -3x + (-2 * x + x * x)) = 7x + -30
(6 + -3x + (-2x + x2)) = 7x + -30

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = 7x + -30

Reorder the terms:
6 + -5x + x2 = -30 + 7x

Solving
6 + -5x + x2 = -30 + 7x

Solving for variable 'x'.

Reorder the terms:
6 + 30 + -5x + -7x + x2 = -30 + 7x + 30 + -7x

Combine like terms: 6 + 30 = 36
36 + -5x + -7x + x2 = -30 + 7x + 30 + -7x

Combine like terms: -5x + -7x = -12x
36 + -12x + x2 = -30 + 7x + 30 + -7x

Reorder the terms:
36 + -12x + x2 = -30 + 30 + 7x + -7x

Combine like terms: -30 + 30 = 0
36 + -12x + x2 = 0 + 7x + -7x
36 + -12x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
36 + -12x + x2 = 0

Factor a trinomial.
(6 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}