(5-2x)(6+3x)=0

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Solution for (5-2x)(6+3x)=0 equation:


Simplifying
(5 + -2x)(6 + 3x) = 0

Multiply (5 + -2x) * (6 + 3x)
(5(6 + 3x) + -2x * (6 + 3x)) = 0
((6 * 5 + 3x * 5) + -2x * (6 + 3x)) = 0
((30 + 15x) + -2x * (6 + 3x)) = 0
(30 + 15x + (6 * -2x + 3x * -2x)) = 0
(30 + 15x + (-12x + -6x2)) = 0

Combine like terms: 15x + -12x = 3x
(30 + 3x + -6x2) = 0

Solving
30 + 3x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(10 + x + -2x2) = 0

Factor a trinomial.
3((5 + -2x)(2 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {2.5, -2}

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