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

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Solution for (7x+3)(5x-4)=0 equation: 


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

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

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

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

Combine like terms: 15x + -28x = -13x
(-12 + -13x + 35x2) = 0

Solving
-12 + -13x + 35x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

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

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

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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 = {-0.4285714286, 0.8}

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