(5X-7)(4X+1)=0

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Solution for (5X-7)(4X+1)=0 equation: 


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

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

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

Multiply (-7 + 5X) * (1 + 4X)
(-7(1 + 4X) + 5X * (1 + 4X)) = 0
((1 * -7 + 4X * -7) + 5X * (1 + 4X)) = 0
((-7 + -28X) + 5X * (1 + 4X)) = 0
(-7 + -28X + (1 * 5X + 4X * 5X)) = 0
(-7 + -28X + (5X + 20X2)) = 0

Combine like terms: -28X + 5X = -23X
(-7 + -23X + 20X2) = 0

Solving
-7 + -23X + 20X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-1 + -4X)(7 + -5X) = 0


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

Simplifying
-1 + -4X = 0

Solving
-1 + -4X = 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 + -4X = 0 + 1

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

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

Divide each side by '-4'.
X = -0.25

Simplifying
X = -0.25

Subproblem 2
Set the factor '(7 + -5X)' equal to zero and attempt to solve:

Simplifying
7 + -5X = 0

Solving
7 + -5X = 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 + -5X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5X = 0 + -7
-5X = 0 + -7

Combine like terms: 0 + -7 = -7
-5X = -7

Divide each side by '-5'.
X = 1.4

Simplifying
X = 1.4
Solution
X = {-0.25, 1.4}

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