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

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


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

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

Multiply (7 + 4x) * (4 + 5x)
(7(4 + 5x) + 4x * (4 + 5x)) = 0
((4 * 7 + 5x * 7) + 4x * (4 + 5x)) = 0
((28 + 35x) + 4x * (4 + 5x)) = 0
(28 + 35x + (4 * 4x + 5x * 4x)) = 0
(28 + 35x + (16x + 20x2)) = 0

Combine like terms: 35x + 16x = 51x
(28 + 51x + 20x2) = 0

Solving
28 + 51x + 20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {-1.75, -0.8}

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