(x-5)(-4x+7)=0

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Solution for (x-5)(-4x+7)=0 equation: 


Simplifying
(x + -5)(-4x + 7) = 0

Reorder the terms:
(-5 + x)(-4x + 7) = 0

Reorder the terms:
(-5 + x)(7 + -4x) = 0

Multiply (-5 + x) * (7 + -4x)
(-5(7 + -4x) + x(7 + -4x)) = 0
((7 * -5 + -4x * -5) + x(7 + -4x)) = 0
((-35 + 20x) + x(7 + -4x)) = 0
(-35 + 20x + (7 * x + -4x * x)) = 0
(-35 + 20x + (7x + -4x2)) = 0

Combine like terms: 20x + 7x = 27x
(-35 + 27x + -4x2) = 0

Solving
-35 + 27x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + x)(7 + -4x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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 = {5, 1.75}

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