(2x+7)(5x-24x+16)=0

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Solution for (2x+7)(5x-24x+16)=0 equation: 


Simplifying
(2x + 7)(5x + -24x + 16) = 0

Reorder the terms:
(7 + 2x)(5x + -24x + 16) = 0

Reorder the terms:
(7 + 2x)(16 + 5x + -24x) = 0

Combine like terms: 5x + -24x = -19x
(7 + 2x)(16 + -19x) = 0

Multiply (7 + 2x) * (16 + -19x)
(7(16 + -19x) + 2x * (16 + -19x)) = 0
((16 * 7 + -19x * 7) + 2x * (16 + -19x)) = 0
((112 + -133x) + 2x * (16 + -19x)) = 0
(112 + -133x + (16 * 2x + -19x * 2x)) = 0
(112 + -133x + (32x + -38x2)) = 0

Combine like terms: -133x + 32x = -101x
(112 + -101x + -38x2) = 0

Solving
112 + -101x + -38x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(16 + -19x)(7 + 2x) = 0


Subproblem 1
Set the factor '(16 + -19x)' equal to zero and attempt to solve:

Simplifying
16 + -19x = 0

Solving
16 + -19x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -19x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -19x = 0 + -16
-19x = 0 + -16

Combine like terms: 0 + -16 = -16
-19x = -16

Divide each side by '-19'.
x = 0.8421052632

Simplifying
x = 0.8421052632

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 = {0.8421052632, -3.5}

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