(2x-5)(4+7x)=0

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Solution for (2x-5)(4+7x)=0 equation: 


Simplifying
(2x + -5)(4 + 7x) = 0

Reorder the terms:
(-5 + 2x)(4 + 7x) = 0

Multiply (-5 + 2x) * (4 + 7x)
(-5(4 + 7x) + 2x * (4 + 7x)) = 0
((4 * -5 + 7x * -5) + 2x * (4 + 7x)) = 0
((-20 + -35x) + 2x * (4 + 7x)) = 0
(-20 + -35x + (4 * 2x + 7x * 2x)) = 0
(-20 + -35x + (8x + 14x2)) = 0

Combine like terms: -35x + 8x = -27x
(-20 + -27x + 14x2) = 0

Solving
-20 + -27x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -7x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

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

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

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

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.5714285714, 2.5}

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