(5x+4)(2x^2-17x-9x)=0

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Solution for (5x+4)(2x^2-17x-9x)=0 equation: 


Simplifying
(5x + 4)(2x2 + -17x + -9x) = 0

Reorder the terms:
(4 + 5x)(2x2 + -17x + -9x) = 0

Reorder the terms:
(4 + 5x)(-17x + -9x + 2x2) = 0

Combine like terms: -17x + -9x = -26x
(4 + 5x)(-26x + 2x2) = 0

Multiply (4 + 5x) * (-26x + 2x2)
(4(-26x + 2x2) + 5x * (-26x + 2x2)) = 0
((-26x * 4 + 2x2 * 4) + 5x * (-26x + 2x2)) = 0
((-104x + 8x2) + 5x * (-26x + 2x2)) = 0
(-104x + 8x2 + (-26x * 5x + 2x2 * 5x)) = 0
(-104x + 8x2 + (-130x2 + 10x3)) = 0

Combine like terms: 8x2 + -130x2 = -122x2
(-104x + -122x2 + 10x3) = 0

Solving
-104x + -122x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-52 + -61x + 5x2) = 0

Factor a trinomial.
2x((-4 + -5x)(13 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {0, -0.8, 13}

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