4(1-7x)(8x+7)=0

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Solution for 4(1-7x)(8x+7)=0 equation: 


Simplifying
4(1 + -7x)(8x + 7) = 0

Reorder the terms:
4(1 + -7x)(7 + 8x) = 0

Multiply (1 + -7x) * (7 + 8x)
4(1(7 + 8x) + -7x * (7 + 8x)) = 0
4((7 * 1 + 8x * 1) + -7x * (7 + 8x)) = 0
4((7 + 8x) + -7x * (7 + 8x)) = 0
4(7 + 8x + (7 * -7x + 8x * -7x)) = 0
4(7 + 8x + (-49x + -56x2)) = 0

Combine like terms: 8x + -49x = -41x
4(7 + -41x + -56x2) = 0
(7 * 4 + -41x * 4 + -56x2 * 4) = 0
(28 + -164x + -224x2) = 0

Solving
28 + -164x + -224x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -41x + -56x2) = 0

Factor a trinomial.
4((1 + -7x)(7 + 8x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 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 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429

Subproblem 2
Set the factor '(7 + 8x)' equal to zero and attempt to solve:

Simplifying
7 + 8x = 0

Solving
7 + 8x = 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 + 8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8x = 0 + -7
8x = 0 + -7

Combine like terms: 0 + -7 = -7
8x = -7

Divide each side by '8'.
x = -0.875

Simplifying
x = -0.875
Solution
x = {0.1428571429, -0.875}

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