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

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


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

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

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

Multiply (3 + x) * (-7 + 2x)
5(3(-7 + 2x) + x(-7 + 2x)) = 0
5((-7 * 3 + 2x * 3) + x(-7 + 2x)) = 0
5((-21 + 6x) + x(-7 + 2x)) = 0
5(-21 + 6x + (-7 * x + 2x * x)) = 0
5(-21 + 6x + (-7x + 2x2)) = 0

Combine like terms: 6x + -7x = -1x
5(-21 + -1x + 2x2) = 0
(-21 * 5 + -1x * 5 + 2x2 * 5) = 0
(-105 + -5x + 10x2) = 0

Solving
-105 + -5x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -1x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 3.5}

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