4(3x-7)(2x+3)=0

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Solution for 4(3x-7)(2x+3)=0 equation: 


Simplifying
4(3x + -7)(2x + 3) = 0

Reorder the terms:
4(-7 + 3x)(2x + 3) = 0

Reorder the terms:
4(-7 + 3x)(3 + 2x) = 0

Multiply (-7 + 3x) * (3 + 2x)
4(-7(3 + 2x) + 3x * (3 + 2x)) = 0
4((3 * -7 + 2x * -7) + 3x * (3 + 2x)) = 0
4((-21 + -14x) + 3x * (3 + 2x)) = 0
4(-21 + -14x + (3 * 3x + 2x * 3x)) = 0
4(-21 + -14x + (9x + 6x2)) = 0

Combine like terms: -14x + 9x = -5x
4(-21 + -5x + 6x2) = 0
(-21 * 4 + -5x * 4 + 6x2 * 4) = 0
(-84 + -20x + 24x2) = 0

Solving
-84 + -20x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -5x + 6x2) = 0

Factor a trinomial.
4((-3 + -2x)(7 + -3x)) = 0

Ignore the factor 4.

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 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.5, 2.333333333}

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