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

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


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

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

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

Multiply (-3 + 7x) * (7 + 5x)
4(-3(7 + 5x) + 7x * (7 + 5x)) = 0
4((7 * -3 + 5x * -3) + 7x * (7 + 5x)) = 0
4((-21 + -15x) + 7x * (7 + 5x)) = 0
4(-21 + -15x + (7 * 7x + 5x * 7x)) = 0
4(-21 + -15x + (49x + 35x2)) = 0

Combine like terms: -15x + 49x = 34x
4(-21 + 34x + 35x2) = 0
(-21 * 4 + 34x * 4 + 35x2 * 4) = 0
(-84 + 136x + 140x2) = 0

Solving
-84 + 136x + 140x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + 34x + 35x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

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

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

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

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-1.4, 0.4285714286}

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