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

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


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

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

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

Multiply (2 + 7x) * (-4 + 5x)
(2(-4 + 5x) + 7x * (-4 + 5x)) = 0
((-4 * 2 + 5x * 2) + 7x * (-4 + 5x)) = 0
((-8 + 10x) + 7x * (-4 + 5x)) = 0
(-8 + 10x + (-4 * 7x + 5x * 7x)) = 0
(-8 + 10x + (-28x + 35x2)) = 0

Combine like terms: 10x + -28x = -18x
(-8 + -18x + 35x2) = 0

Solving
-8 + -18x + 35x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-2 + -7x)' equal to zero and attempt to solve:

Simplifying
-2 + -7x = 0

Solving
-2 + -7x = 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 + -7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x = 0 + 2
-7x = 0 + 2

Combine like terms: 0 + 2 = 2
-7x = 2

Divide each side by '-7'.
x = -0.2857142857

Simplifying
x = -0.2857142857

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 = {-0.2857142857, 0.8}

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