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

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


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

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

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

Multiply (2 + 5x) * (-3 + 2x)
2(2(-3 + 2x) + 5x * (-3 + 2x)) = 0
2((-3 * 2 + 2x * 2) + 5x * (-3 + 2x)) = 0
2((-6 + 4x) + 5x * (-3 + 2x)) = 0
2(-6 + 4x + (-3 * 5x + 2x * 5x)) = 0
2(-6 + 4x + (-15x + 10x2)) = 0

Combine like terms: 4x + -15x = -11x
2(-6 + -11x + 10x2) = 0
(-6 * 2 + -11x * 2 + 10x2 * 2) = 0
(-12 + -22x + 20x2) = 0

Solving
-12 + -22x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -11x + 10x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

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 = {-0.4, 1.5}

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