(4x+2)(-10x+9)=0

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Solution for (4x+2)(-10x+9)=0 equation: 


Simplifying
(4x + 2)(-10x + 9) = 0

Reorder the terms:
(2 + 4x)(-10x + 9) = 0

Reorder the terms:
(2 + 4x)(9 + -10x) = 0

Multiply (2 + 4x) * (9 + -10x)
(2(9 + -10x) + 4x * (9 + -10x)) = 0
((9 * 2 + -10x * 2) + 4x * (9 + -10x)) = 0
((18 + -20x) + 4x * (9 + -10x)) = 0
(18 + -20x + (9 * 4x + -10x * 4x)) = 0
(18 + -20x + (36x + -40x2)) = 0

Combine like terms: -20x + 36x = 16x
(18 + 16x + -40x2) = 0

Solving
18 + 16x + -40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 8x + -20x2) = 0

Factor a trinomial.
2((9 + -10x)(1 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -10x)' equal to zero and attempt to solve:

Simplifying
9 + -10x = 0

Solving
9 + -10x = 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 + -10x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -10x = 0 + -9
-10x = 0 + -9

Combine like terms: 0 + -9 = -9
-10x = -9

Divide each side by '-10'.
x = 0.9

Simplifying
x = 0.9

Subproblem 2
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
Solution
x = {0.9, -0.5}

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