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

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


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

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

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

Multiply (-9 + 4x) * (2 + 2x)
(-9(2 + 2x) + 4x * (2 + 2x)) = 0
((2 * -9 + 2x * -9) + 4x * (2 + 2x)) = 0
((-18 + -18x) + 4x * (2 + 2x)) = 0
(-18 + -18x + (2 * 4x + 2x * 4x)) = 0
(-18 + -18x + (8x + 8x2)) = 0

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

Solving
-18 + -10x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -5x + 4x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

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 = {-1, 2.25}

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