4(3x-7)(5x+2)=0

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Solution for 4(3x-7)(5x+2)=0 equation: 


Simplifying
4(3x + -7)(5x + 2) = 0

Reorder the terms:
4(-7 + 3x)(5x + 2) = 0

Reorder the terms:
4(-7 + 3x)(2 + 5x) = 0

Multiply (-7 + 3x) * (2 + 5x)
4(-7(2 + 5x) + 3x * (2 + 5x)) = 0
4((2 * -7 + 5x * -7) + 3x * (2 + 5x)) = 0
4((-14 + -35x) + 3x * (2 + 5x)) = 0
4(-14 + -35x + (2 * 3x + 5x * 3x)) = 0
4(-14 + -35x + (6x + 15x2)) = 0

Combine like terms: -35x + 6x = -29x
4(-14 + -29x + 15x2) = 0
(-14 * 4 + -29x * 4 + 15x2 * 4) = 0
(-56 + -116x + 60x2) = 0

Solving
-56 + -116x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -29x + 15x2) = 0

Factor a trinomial.
4((-2 + -5x)(7 + -3x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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 = {-0.4, 2.333333333}

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