-(2x+3)(5x+7)=0

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Solution for -(2x+3)(5x+7)=0 equation: 


Simplifying
-1(2x + 3)(5x + 7) = 0

Reorder the terms:
-1(3 + 2x)(5x + 7) = 0

Reorder the terms:
-1(3 + 2x)(7 + 5x) = 0

Multiply (3 + 2x) * (7 + 5x)
-1(3(7 + 5x) + 2x * (7 + 5x)) = 0
-1((7 * 3 + 5x * 3) + 2x * (7 + 5x)) = 0
-1((21 + 15x) + 2x * (7 + 5x)) = 0
-1(21 + 15x + (7 * 2x + 5x * 2x)) = 0
-1(21 + 15x + (14x + 10x2)) = 0

Combine like terms: 15x + 14x = 29x
-1(21 + 29x + 10x2) = 0
(21 * -1 + 29x * -1 + 10x2 * -1) = 0
(-21 + -29x + -10x2) = 0

Solving
-21 + -29x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 29x + 10x2) = 0

Factor a trinomial.
-1((3 + 2x)(7 + 5x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve:

Simplifying
7 + 5x = 0

Solving
7 + 5x = 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 + 5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 0 + -7
5x = 0 + -7

Combine like terms: 0 + -7 = -7
5x = -7

Divide each side by '5'.
x = -1.4

Simplifying
x = -1.4
Solution
x = {-1.5, -1.4}

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