3(5x-7)(2x+3)=0

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Solution for 3(5x-7)(2x+3)=0 equation: 


Simplifying
3(5x + -7)(2x + 3) = 0

Reorder the terms:
3(-7 + 5x)(2x + 3) = 0

Reorder the terms:
3(-7 + 5x)(3 + 2x) = 0

Multiply (-7 + 5x) * (3 + 2x)
3(-7(3 + 2x) + 5x * (3 + 2x)) = 0
3((3 * -7 + 2x * -7) + 5x * (3 + 2x)) = 0
3((-21 + -14x) + 5x * (3 + 2x)) = 0
3(-21 + -14x + (3 * 5x + 2x * 5x)) = 0
3(-21 + -14x + (15x + 10x2)) = 0

Combine like terms: -14x + 15x = 1x
3(-21 + 1x + 10x2) = 0
(-21 * 3 + 1x * 3 + 10x2 * 3) = 0
(-63 + 3x + 30x2) = 0

Solving
-63 + 3x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + x + 10x2) = 0

Factor a trinomial.
3((-3 + -2x)(7 + -5x)) = 0

Ignore the factor 3.

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 '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-1.5, 1.4}

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