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

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


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

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

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

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

Combine like terms: 8x + -7x = 1x
0 = (-28 + 1x + 2x2)

Solving
0 = -28 + 1x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 28 = 28
28 + -1x + -2x2 = -28 + 1x + 2x2 + 28 + -1x + -2x2

Reorder the terms:
28 + -1x + -2x2 = -28 + 28 + 1x + -1x + 2x2 + -2x2

Combine like terms: -28 + 28 = 0
28 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
28 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
28 + -1x + -2x2 = 0 + 2x2 + -2x2
28 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
28 + -1x + -2x2 = 0

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


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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {3.5, -4}

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