(x-3)(4x+9)=0

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Solution for (x-3)(4x+9)=0 equation:


Simplifying
(x + -3)(4x + 9) = 0

Reorder the terms:
(-3 + x)(4x + 9) = 0

Reorder the terms:
(-3 + x)(9 + 4x) = 0

Multiply (-3 + x) * (9 + 4x)
(-3(9 + 4x) + x(9 + 4x)) = 0
((9 * -3 + 4x * -3) + x(9 + 4x)) = 0
((-27 + -12x) + x(9 + 4x)) = 0
(-27 + -12x + (9 * x + 4x * x)) = 0
(-27 + -12x + (9x + 4x2)) = 0

Combine like terms: -12x + 9x = -3x
(-27 + -3x + 4x2) = 0

Solving
-27 + -3x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -4x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-2.25, 3}

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