(4x-9)(10x+5)=0

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Solution for (4x-9)(10x+5)=0 equation: 


Simplifying
(4x + -9)(10x + 5) = 0

Reorder the terms:
(-9 + 4x)(10x + 5) = 0

Reorder the terms:
(-9 + 4x)(5 + 10x) = 0

Multiply (-9 + 4x) * (5 + 10x)
(-9(5 + 10x) + 4x * (5 + 10x)) = 0
((5 * -9 + 10x * -9) + 4x * (5 + 10x)) = 0
((-45 + -90x) + 4x * (5 + 10x)) = 0
(-45 + -90x + (5 * 4x + 10x * 4x)) = 0
(-45 + -90x + (20x + 40x2)) = 0

Combine like terms: -90x + 20x = -70x
(-45 + -70x + 40x2) = 0

Solving
-45 + -70x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + -14x + 8x2) = 0

Factor a trinomial.
5((-1 + -2x)(9 + -4x)) = 0

Ignore the factor 5.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-0.5, 2.25}

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