(6+4x)*(15x+25)=0

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Solution for (6+4x)*(15x+25)=0 equation:


Simplifying
(6 + 4x)(15x + 25) = 0

Reorder the terms:
(6 + 4x)(25 + 15x) = 0

Multiply (6 + 4x) * (25 + 15x)
(6(25 + 15x) + 4x * (25 + 15x)) = 0
((25 * 6 + 15x * 6) + 4x * (25 + 15x)) = 0
((150 + 90x) + 4x * (25 + 15x)) = 0
(150 + 90x + (25 * 4x + 15x * 4x)) = 0
(150 + 90x + (100x + 60x2)) = 0

Combine like terms: 90x + 100x = 190x
(150 + 190x + 60x2) = 0

Solving
150 + 190x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(15 + 19x + 6x2) = 0

Factor a trinomial.
10((5 + 3x)(3 + 2x)) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 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 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {-1.666666667, -1.5}

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