(7x-3)(5x+12)=0

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Solution for (7x-3)(5x+12)=0 equation: 


Simplifying
(7x + -3)(5x + 12) = 0

Reorder the terms:
(-3 + 7x)(5x + 12) = 0

Reorder the terms:
(-3 + 7x)(12 + 5x) = 0

Multiply (-3 + 7x) * (12 + 5x)
(-3(12 + 5x) + 7x * (12 + 5x)) = 0
((12 * -3 + 5x * -3) + 7x * (12 + 5x)) = 0
((-36 + -15x) + 7x * (12 + 5x)) = 0
(-36 + -15x + (12 * 7x + 5x * 7x)) = 0
(-36 + -15x + (84x + 35x2)) = 0

Combine like terms: -15x + 84x = 69x
(-36 + 69x + 35x2) = 0

Solving
-36 + 69x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -5x)(3 + -7x) = 0


Subproblem 1
Set the factor '(-12 + -5x)' equal to zero and attempt to solve:

Simplifying
-12 + -5x = 0

Solving
-12 + -5x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -5x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -5x = 0 + 12
-5x = 0 + 12

Combine like terms: 0 + 12 = 12
-5x = 12

Divide each side by '-5'.
x = -2.4

Simplifying
x = -2.4

Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-2.4, 0.4285714286}

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