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

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


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

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

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

Combine like terms: -2x + 36x = 34x
(-18 + 34x + 4x2) = 0

Solving
-18 + 34x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 17x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -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 = {-9, 0.5}

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