(4x+7)(-5x-10)=0

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Solution for (4x+7)(-5x-10)=0 equation: 


Simplifying
(4x + 7)(-5x + -10) = 0

Reorder the terms:
(7 + 4x)(-5x + -10) = 0

Reorder the terms:
(7 + 4x)(-10 + -5x) = 0

Multiply (7 + 4x) * (-10 + -5x)
(7(-10 + -5x) + 4x * (-10 + -5x)) = 0
((-10 * 7 + -5x * 7) + 4x * (-10 + -5x)) = 0
((-70 + -35x) + 4x * (-10 + -5x)) = 0
(-70 + -35x + (-10 * 4x + -5x * 4x)) = 0
(-70 + -35x + (-40x + -20x2)) = 0

Combine like terms: -35x + -40x = -75x
(-70 + -75x + -20x2) = 0

Solving
-70 + -75x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-5'.
-5(14 + 15x + 4x2) = 0

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

Ignore the factor -5.

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2

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 = {-2, -1.75}

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