(2x-5)(3x+7)=35

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Solution for (2x-5)(3x+7)=35 equation: 


Simplifying
(2x + -5)(3x + 7) = 35

Reorder the terms:
(-5 + 2x)(3x + 7) = 35

Reorder the terms:
(-5 + 2x)(7 + 3x) = 35

Multiply (-5 + 2x) * (7 + 3x)
(-5(7 + 3x) + 2x * (7 + 3x)) = 35
((7 * -5 + 3x * -5) + 2x * (7 + 3x)) = 35
((-35 + -15x) + 2x * (7 + 3x)) = 35
(-35 + -15x + (7 * 2x + 3x * 2x)) = 35
(-35 + -15x + (14x + 6x2)) = 35

Combine like terms: -15x + 14x = -1x
(-35 + -1x + 6x2) = 35

Solving
-35 + -1x + 6x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -35 + -1x + 6x2 = 35 + -35

Combine like terms: -35 + -35 = -70
-70 + -1x + 6x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-70 + -1x + 6x2 = 0

Factor a trinomial.
(-10 + -3x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333

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 = {-3.333333333, 3.5}

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