7(2-5x)(3x+1)=0

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Solution for 7(2-5x)(3x+1)=0 equation: 


Simplifying
7(2 + -5x)(3x + 1) = 0

Reorder the terms:
7(2 + -5x)(1 + 3x) = 0

Multiply (2 + -5x) * (1 + 3x)
7(2(1 + 3x) + -5x * (1 + 3x)) = 0
7((1 * 2 + 3x * 2) + -5x * (1 + 3x)) = 0
7((2 + 6x) + -5x * (1 + 3x)) = 0
7(2 + 6x + (1 * -5x + 3x * -5x)) = 0
7(2 + 6x + (-5x + -15x2)) = 0

Combine like terms: 6x + -5x = 1x
7(2 + 1x + -15x2) = 0
(2 * 7 + 1x * 7 + -15x2 * 7) = 0
(14 + 7x + -105x2) = 0

Solving
14 + 7x + -105x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(2 + x + -15x2) = 0

Factor a trinomial.
7((2 + -5x)(1 + 3x)) = 0

Ignore the factor 7.

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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {0.4, -0.3333333333}

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