(2x+7)(5x-6)=0

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Solution for (2x+7)(5x-6)=0 equation: 


Simplifying
(2x + 7)(5x + -6) = 0

Reorder the terms:
(7 + 2x)(5x + -6) = 0

Reorder the terms:
(7 + 2x)(-6 + 5x) = 0

Multiply (7 + 2x) * (-6 + 5x)
(7(-6 + 5x) + 2x * (-6 + 5x)) = 0
((-6 * 7 + 5x * 7) + 2x * (-6 + 5x)) = 0
((-42 + 35x) + 2x * (-6 + 5x)) = 0
(-42 + 35x + (-6 * 2x + 5x * 2x)) = 0
(-42 + 35x + (-12x + 10x2)) = 0

Combine like terms: 35x + -12x = 23x
(-42 + 23x + 10x2) = 0

Solving
-42 + 23x + 10x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -2x)(6 + -5x) = 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 '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-3.5, 1.2}

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