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

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


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

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

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

Multiply (-7 + 4x) * (7 + 2x)
4(-7(7 + 2x) + 4x * (7 + 2x)) = 0
4((7 * -7 + 2x * -7) + 4x * (7 + 2x)) = 0
4((-49 + -14x) + 4x * (7 + 2x)) = 0
4(-49 + -14x + (7 * 4x + 2x * 4x)) = 0
4(-49 + -14x + (28x + 8x2)) = 0

Combine like terms: -14x + 28x = 14x
4(-49 + 14x + 8x2) = 0
(-49 * 4 + 14x * 4 + 8x2 * 4) = 0
(-196 + 56x + 32x2) = 0

Solving
-196 + 56x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-49 + 14x + 8x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-3.5, 1.75}

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