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

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


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

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

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

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

Combine like terms: 4x + -28x = -24x
(-14 + -24x + 8x2) = 0

Solving
-14 + -24x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -12x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.5, 3.5}

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