(2x-7)(x)=30

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

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

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

Reorder the terms for easier multiplication:
x(-7 + 2x) = 30
(-7 * x + 2x * x) = 30
(-7x + 2x2) = 30

Solving
-7x + 2x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -7x + 2x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -7x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
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 = {-2.5, 6}