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

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


Simplifying
(4x + -5)(-1x + -7) = 0

Reorder the terms:
(-5 + 4x)(-1x + -7) = 0

Reorder the terms:
(-5 + 4x)(-7 + -1x) = 0

Multiply (-5 + 4x) * (-7 + -1x)
(-5(-7 + -1x) + 4x * (-7 + -1x)) = 0
((-7 * -5 + -1x * -5) + 4x * (-7 + -1x)) = 0
((35 + 5x) + 4x * (-7 + -1x)) = 0
(35 + 5x + (-7 * 4x + -1x * 4x)) = 0
(35 + 5x + (-28x + -4x2)) = 0

Combine like terms: 5x + -28x = -23x
(35 + -23x + -4x2) = 0

Solving
35 + -23x + -4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7
Solution
x = {1.25, -7}

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