4(2x+1)(2x-9)=0

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Solution for 4(2x+1)(2x-9)=0 equation: 


Simplifying
4(2x + 1)(2x + -9) = 0

Reorder the terms:
4(1 + 2x)(2x + -9) = 0

Reorder the terms:
4(1 + 2x)(-9 + 2x) = 0

Multiply (1 + 2x) * (-9 + 2x)
4(1(-9 + 2x) + 2x * (-9 + 2x)) = 0
4((-9 * 1 + 2x * 1) + 2x * (-9 + 2x)) = 0
4((-9 + 2x) + 2x * (-9 + 2x)) = 0
4(-9 + 2x + (-9 * 2x + 2x * 2x)) = 0
4(-9 + 2x + (-18x + 4x2)) = 0

Combine like terms: 2x + -18x = -16x
4(-9 + -16x + 4x2) = 0
(-9 * 4 + -16x * 4 + 4x2 * 4) = 0
(-36 + -64x + 16x2) = 0

Solving
-36 + -64x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -16x + 4x2) = 0

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

Ignore the factor 4.

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 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-0.5, 4.5}

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