(2x-3)(x-7)=90

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Solution for (2x-3)(x-7)=90 equation: 


Simplifying
(2x + -3)(x + -7) = 90

Reorder the terms:
(-3 + 2x)(x + -7) = 90

Reorder the terms:
(-3 + 2x)(-7 + x) = 90

Multiply (-3 + 2x) * (-7 + x)
(-3(-7 + x) + 2x * (-7 + x)) = 90
((-7 * -3 + x * -3) + 2x * (-7 + x)) = 90
((21 + -3x) + 2x * (-7 + x)) = 90
(21 + -3x + (-7 * 2x + x * 2x)) = 90
(21 + -3x + (-14x + 2x2)) = 90

Combine like terms: -3x + -14x = -17x
(21 + -17x + 2x2) = 90

Solving
21 + -17x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
21 + -90 + -17x + 2x2 = 90 + -90

Combine like terms: 21 + -90 = -69
-69 + -17x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-69 + -17x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(23 + -2x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(23 + -2x)' equal to zero and attempt to solve:

Simplifying
23 + -2x = 0

Solving
23 + -2x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -2x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -2x = 0 + -23
-2x = 0 + -23

Combine like terms: 0 + -23 = -23
-2x = -23

Divide each side by '-2'.
x = 11.5

Simplifying
x = 11.5
Solution
x = {-3, 11.5}

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