(2x-7)(2x-8)=0

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Solution for (2x-7)(2x-8)=0 equation: 


Simplifying
(2x + -7)(2x + -8) = 0

Reorder the terms:
(-7 + 2x)(2x + -8) = 0

Reorder the terms:
(-7 + 2x)(-8 + 2x) = 0

Multiply (-7 + 2x) * (-8 + 2x)
(-7(-8 + 2x) + 2x * (-8 + 2x)) = 0
((-8 * -7 + 2x * -7) + 2x * (-8 + 2x)) = 0
((56 + -14x) + 2x * (-8 + 2x)) = 0
(56 + -14x + (-8 * 2x + 2x * 2x)) = 0
(56 + -14x + (-16x + 4x2)) = 0

Combine like terms: -14x + -16x = -30x
(56 + -30x + 4x2) = 0

Solving
56 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -15x + 2x2) = 0

Factor a trinomial.
2((7 + -2x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3.5, 4}

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