(3x+7)(5x+4)=

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Solution for (3x+7)(5x+4)= equation: 


Simplifying
(3x + 7)(5x + 4) = 0

Reorder the terms:
(7 + 3x)(5x + 4) = 0

Reorder the terms:
(7 + 3x)(4 + 5x) = 0

Multiply (7 + 3x) * (4 + 5x)
(7(4 + 5x) + 3x * (4 + 5x)) = 0
((4 * 7 + 5x * 7) + 3x * (4 + 5x)) = 0
((28 + 35x) + 3x * (4 + 5x)) = 0
(28 + 35x + (4 * 3x + 5x * 3x)) = 0
(28 + 35x + (12x + 15x2)) = 0

Combine like terms: 35x + 12x = 47x
(28 + 47x + 15x2) = 0

Solving
28 + 47x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 3x)(4 + 5x) = 0


Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, -0.8}

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