(2x-3)(2x+31)=0

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Solution for (2x-3)(2x+31)=0 equation: 


Simplifying
(2x + -3)(2x + 31) = 0

Reorder the terms:
(-3 + 2x)(2x + 31) = 0

Reorder the terms:
(-3 + 2x)(31 + 2x) = 0

Multiply (-3 + 2x) * (31 + 2x)
(-3(31 + 2x) + 2x * (31 + 2x)) = 0
((31 * -3 + 2x * -3) + 2x * (31 + 2x)) = 0
((-93 + -6x) + 2x * (31 + 2x)) = 0
(-93 + -6x + (31 * 2x + 2x * 2x)) = 0
(-93 + -6x + (62x + 4x2)) = 0

Combine like terms: -6x + 62x = 56x
(-93 + 56x + 4x2) = 0

Solving
-93 + 56x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-31 + -2x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-31 + -2x)' equal to zero and attempt to solve:

Simplifying
-31 + -2x = 0

Solving
-31 + -2x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2x = 0 + 31
-2x = 0 + 31

Combine like terms: 0 + 31 = 31
-2x = 31

Divide each side by '-2'.
x = -15.5

Simplifying
x = -15.5

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-15.5, 1.5}

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