(2x-3)(x+6)=-18

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Solution for (2x-3)(x+6)=-18 equation:


Simplifying
(2x + -3)(x + 6) = -18

Reorder the terms:
(-3 + 2x)(x + 6) = -18

Reorder the terms:
(-3 + 2x)(6 + x) = -18

Multiply (-3 + 2x) * (6 + x)
(-3(6 + x) + 2x * (6 + x)) = -18
((6 * -3 + x * -3) + 2x * (6 + x)) = -18
((-18 + -3x) + 2x * (6 + x)) = -18
(-18 + -3x + (6 * 2x + x * 2x)) = -18
(-18 + -3x + (12x + 2x2)) = -18

Combine like terms: -3x + 12x = 9x
(-18 + 9x + 2x2) = -18

Add '18' to each side of the equation.
-18 + 9x + 18 + 2x2 = -18 + 18

Reorder the terms:
-18 + 18 + 9x + 2x2 = -18 + 18

Combine like terms: -18 + 18 = 0
0 + 9x + 2x2 = -18 + 18
9x + 2x2 = -18 + 18

Combine like terms: -18 + 18 = 0
9x + 2x2 = 0

Solving
9x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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, -4.5}

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