(2x-3)(2x-7)=0

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Solution for (2x-3)(2x-7)=0 equation: 


Simplifying
(2x + -3)(2x + -7) = 0

Reorder the terms:
(-3 + 2x)(2x + -7) = 0

Reorder the terms:
(-3 + 2x)(-7 + 2x) = 0

Multiply (-3 + 2x) * (-7 + 2x)
(-3(-7 + 2x) + 2x * (-7 + 2x)) = 0
((-7 * -3 + 2x * -3) + 2x * (-7 + 2x)) = 0
((21 + -6x) + 2x * (-7 + 2x)) = 0
(21 + -6x + (-7 * 2x + 2x * 2x)) = 0
(21 + -6x + (-14x + 4x2)) = 0

Combine like terms: -6x + -14x = -20x
(21 + -20x + 4x2) = 0

Solving
21 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(7 + -2x) = 0


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

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

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

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1.5, 3.5}

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