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

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


Simplifying
(4x2 + 7x)(5x2 + -3x) = 0

Reorder the terms:
(7x + 4x2)(5x2 + -3x) = 0

Reorder the terms:
(7x + 4x2)(-3x + 5x2) = 0

Multiply (7x + 4x2) * (-3x + 5x2)
(7x * (-3x + 5x2) + 4x2 * (-3x + 5x2)) = 0
((-3x * 7x + 5x2 * 7x) + 4x2 * (-3x + 5x2)) = 0
((-21x2 + 35x3) + 4x2 * (-3x + 5x2)) = 0
(-21x2 + 35x3 + (-3x * 4x2 + 5x2 * 4x2)) = 0
(-21x2 + 35x3 + (-12x3 + 20x4)) = 0

Combine like terms: 35x3 + -12x3 = 23x3
(-21x2 + 23x3 + 20x4) = 0

Solving
-21x2 + 23x3 + 20x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-21 + 23x + 20x2) = 0

Factor a trinomial.
x2((-7 + -4x)(3 + -5x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
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 3
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, -1.75, 0.6}

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