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

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


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

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

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

Multiply (-4 + x) * (9 + 4x)
(-4(9 + 4x) + x(9 + 4x)) = 0
((9 * -4 + 4x * -4) + x(9 + 4x)) = 0
((-36 + -16x) + x(9 + 4x)) = 0
(-36 + -16x + (9 * x + 4x * x)) = 0
(-36 + -16x + (9x + 4x2)) = 0

Combine like terms: -16x + 9x = -7x
(-36 + -7x + 4x2) = 0

Solving
-36 + -7x + 4x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2.25, 4}

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