(4x+10)(3x-15)=0

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Solution for (4x+10)(3x-15)=0 equation: 


Simplifying
(4x + 10)(3x + -15) = 0

Reorder the terms:
(10 + 4x)(3x + -15) = 0

Reorder the terms:
(10 + 4x)(-15 + 3x) = 0

Multiply (10 + 4x) * (-15 + 3x)
(10(-15 + 3x) + 4x * (-15 + 3x)) = 0
((-15 * 10 + 3x * 10) + 4x * (-15 + 3x)) = 0
((-150 + 30x) + 4x * (-15 + 3x)) = 0
(-150 + 30x + (-15 * 4x + 3x * 4x)) = 0
(-150 + 30x + (-60x + 12x2)) = 0

Combine like terms: 30x + -60x = -30x
(-150 + -30x + 12x2) = 0

Solving
-150 + -30x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-25 + -5x + 2x2) = 0

Factor a trinomial.
6((-5 + -2x)(5 + -1x)) = 0

Ignore the factor 6.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2.5, 5}

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