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

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


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

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

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

Multiply (-3 + 2x) * (7 + 4x)
5(-3(7 + 4x) + 2x * (7 + 4x)) = 0
5((7 * -3 + 4x * -3) + 2x * (7 + 4x)) = 0
5((-21 + -12x) + 2x * (7 + 4x)) = 0
5(-21 + -12x + (7 * 2x + 4x * 2x)) = 0
5(-21 + -12x + (14x + 8x2)) = 0

Combine like terms: -12x + 14x = 2x
5(-21 + 2x + 8x2) = 0
(-21 * 5 + 2x * 5 + 8x2 * 5) = 0
(-105 + 10x + 40x2) = 0

Solving
-105 + 10x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + 2x + 8x2) = 0

Factor a trinomial.
5((-7 + -4x)(3 + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

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

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

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

Subproblem 2
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
Solution
x = {-1.75, 1.5}

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