(5x+8)(2x-7)=0

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Solution for (5x+8)(2x-7)=0 equation: 


Simplifying
(5x + 8)(2x + -7) = 0

Reorder the terms:
(8 + 5x)(2x + -7) = 0

Reorder the terms:
(8 + 5x)(-7 + 2x) = 0

Multiply (8 + 5x) * (-7 + 2x)
(8(-7 + 2x) + 5x * (-7 + 2x)) = 0
((-7 * 8 + 2x * 8) + 5x * (-7 + 2x)) = 0
((-56 + 16x) + 5x * (-7 + 2x)) = 0
(-56 + 16x + (-7 * 5x + 2x * 5x)) = 0
(-56 + 16x + (-35x + 10x2)) = 0

Combine like terms: 16x + -35x = -19x
(-56 + -19x + 10x2) = 0

Solving
-56 + -19x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -5x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6

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

Simplifying
7 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.6, 3.5}

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