4(2x+7)(2x-1)=0

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Solution for 4(2x+7)(2x-1)=0 equation: 


Simplifying
4(2x + 7)(2x + -1) = 0

Reorder the terms:
4(7 + 2x)(2x + -1) = 0

Reorder the terms:
4(7 + 2x)(-1 + 2x) = 0

Multiply (7 + 2x) * (-1 + 2x)
4(7(-1 + 2x) + 2x * (-1 + 2x)) = 0
4((-1 * 7 + 2x * 7) + 2x * (-1 + 2x)) = 0
4((-7 + 14x) + 2x * (-1 + 2x)) = 0
4(-7 + 14x + (-1 * 2x + 2x * 2x)) = 0
4(-7 + 14x + (-2x + 4x2)) = 0

Combine like terms: 14x + -2x = 12x
4(-7 + 12x + 4x2) = 0
(-7 * 4 + 12x * 4 + 4x2 * 4) = 0
(-28 + 48x + 16x2) = 0

Solving
-28 + 48x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + 12x + 4x2) = 0

Factor a trinomial.
4((-7 + -2x)(1 + -2x)) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3.5, 0.5}

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