(2x-2)(4x-7)=0

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Solution for (2x-2)(4x-7)=0 equation: 


Simplifying
(2x + -2)(4x + -7) = 0

Reorder the terms:
(-2 + 2x)(4x + -7) = 0

Reorder the terms:
(-2 + 2x)(-7 + 4x) = 0

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

Combine like terms: -8x + -14x = -22x
(14 + -22x + 8x2) = 0

Solving
14 + -22x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -11x + 4x2) = 0

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

Ignore the factor 2.

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 '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {1, 1.75}

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