(10x+15)(12x-3)=

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Solution for (10x+15)(12x-3)= equation: 


Simplifying
(10x + 15)(12x + -3) = 0

Reorder the terms:
(15 + 10x)(12x + -3) = 0

Reorder the terms:
(15 + 10x)(-3 + 12x) = 0

Multiply (15 + 10x) * (-3 + 12x)
(15(-3 + 12x) + 10x * (-3 + 12x)) = 0
((-3 * 15 + 12x * 15) + 10x * (-3 + 12x)) = 0
((-45 + 180x) + 10x * (-3 + 12x)) = 0
(-45 + 180x + (-3 * 10x + 12x * 10x)) = 0
(-45 + 180x + (-30x + 120x2)) = 0

Combine like terms: 180x + -30x = 150x
(-45 + 150x + 120x2) = 0

Solving
-45 + 150x + 120x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-3 + 10x + 8x2) = 0

Factor a trinomial.
15((-3 + -2x)(1 + -4x)) = 0

Ignore the factor 15.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {-1.5, 0.25}

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