(7x+4)(2x-5x-3)=0

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Solution for (7x+4)(2x-5x-3)=0 equation: 


Simplifying
(7x + 4)(2x + -5x + -3) = 0

Reorder the terms:
(4 + 7x)(2x + -5x + -3) = 0

Reorder the terms:
(4 + 7x)(-3 + 2x + -5x) = 0

Combine like terms: 2x + -5x = -3x
(4 + 7x)(-3 + -3x) = 0

Multiply (4 + 7x) * (-3 + -3x)
(4(-3 + -3x) + 7x * (-3 + -3x)) = 0
((-3 * 4 + -3x * 4) + 7x * (-3 + -3x)) = 0
((-12 + -12x) + 7x * (-3 + -3x)) = 0
(-12 + -12x + (-3 * 7x + -3x * 7x)) = 0
(-12 + -12x + (-21x + -21x2)) = 0

Combine like terms: -12x + -21x = -33x
(-12 + -33x + -21x2) = 0

Solving
-12 + -33x + -21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(4 + 11x + 7x2) = 0

Factor a trinomial.
-3((1 + x)(4 + 7x)) = 0

Ignore the factor -3.

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(4 + 7x)' equal to zero and attempt to solve:

Simplifying
4 + 7x = 0

Solving
4 + 7x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7x = 0 + -4
7x = 0 + -4

Combine like terms: 0 + -4 = -4
7x = -4

Divide each side by '7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
Solution
x = {-1, -0.5714285714}

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