(2x-7)(x-3)=10

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Solution for (2x-7)(x-3)=10 equation: 


Simplifying
(2x + -7)(x + -3) = 10

Reorder the terms:
(-7 + 2x)(x + -3) = 10

Reorder the terms:
(-7 + 2x)(-3 + x) = 10

Multiply (-7 + 2x) * (-3 + x)
(-7(-3 + x) + 2x * (-3 + x)) = 10
((-3 * -7 + x * -7) + 2x * (-3 + x)) = 10
((21 + -7x) + 2x * (-3 + x)) = 10
(21 + -7x + (-3 * 2x + x * 2x)) = 10
(21 + -7x + (-6x + 2x2)) = 10

Combine like terms: -7x + -6x = -13x
(21 + -13x + 2x2) = 10

Solving
21 + -13x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
21 + -10 + -13x + 2x2 = 10 + -10

Combine like terms: 21 + -10 = 11
11 + -13x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
11 + -13x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(11 + -2x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {1, 5.5}

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